TI-83 Plus Silver Edition
Graphing Calculator Guidebook
TI
First Steps
Creating…
Beyond the Basics
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07/23/03
© 2001-2003 Texas Instruments
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TI-83 Plus
Chapter 1:
Operating the TI-83 Plus Silver Edition
Documentation Conventions
In the body of this guidebook, TI-83 Plus (in silver) refers to the
TI-83 Plus Silver Edition. Sometimes, as in Chapter 19, the full
name TI-83 Plus Silver Edition is used to distinguish it from the
TI-83 Plus.
All the instructions and examples in this guidebook also work for
the TI-83 Plus. All the functions of the TI-83 Plus Silver Edition and the
TI-83 Plus are the same. The two calculators differ only in available RAM
memory and Flash application ROM memory.
TI-83 Plus
Operating the TI-83 Plus Silver Edition
1
TI-83 Plus Keyboard
Generally, the keyboard is divided into these zones: graphing keys,
editing keys, advanced function keys, and scientific calculator keys.
Keyboard Zones
Graphing — Graphing keys access the interactive graphing features.
Editing — Editing keys allow you to edit expressions and values.
Advanced — Advanced function keys display menus that access the
advanced functions.
Scientific — Scientific calculator keys access the capabilities of a
standard scientific calculator.
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Operating the TI-83 Plus Silver Edition
2
TI-83 Plus
Graphing Keys
Editing Keys
Advanced
Function Keys
Scientific
Calculator Keys
Colors may vary in actual product.
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Operating the TI-83 Plus Silver Edition
3
Using the Color.Coded Keyboard
The keys on the TI-83 Plus are color-coded to help you easily locate the
key you need.
The light gray keys are the number keys. The blue keys along the right side
of the keyboard are the common math functions. The blue keys across the
top set up and display graphs. The blue Πkey provides access to
applications such as the Finance application.
The primary function of each key is printed on the keys. For example,
when you press , the MATH menu is displayed.
Using the y and ƒ Keys
The secondary function of each key is printed in yellow above the key.
When you press the yellow y key, the character, abbreviation, or word
printed in yellow above the other keys becomes active for the next
keystroke. For example, when you press y and then , the TEST
menu is displayed. This guidebook describes this keystroke combination
as y :.
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Operating the TI-83 Plus Silver Edition
4
The alpha function of each key is printed in green above the key. When
you press the green ƒ key, the alpha character printed in green
above the other keys becomes active for the next keystroke. For
example, when you press ƒ and then , the letter A is entered.
This guidebook describes this keystroke combination as ƒ [A].
The y key
accesses the
second function
printed in yellow
above each key.
The ƒ key
accesses the alpha
function printed in
green above each
key.
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Operating the TI-83 Plus Silver Edition
5
Turning On and Turning Off the TI-83 Plus
Turning On the Calculator
To turn on the TI-83 Plus, press É.
• If you previously had turned off the
calculator by pressing y M, the
TI-83 Plus displays the home screen as it
was when you last used it and clears any
error.
• If Automatic Power Down™ (APDé) had previously turned off the
calculator, the TI-83 Plus will return exactly as you left it, including the
display, cursor, and any error.
• If the TI-83 Plus is turned off and you connect it to another calculator
or personal computer, the TI-83 Plus will “wake up” when you
complete the connection.
• If the TI-83 Plus is turned off and connected to another calculator or
personal computer, any communication activity will “wake up” the
TI-83 Plus.
To prolong the life of the batteries, APD turns off the TI-83 Plus
automatically after about five minutes without any activity.
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Operating the TI-83 Plus Silver Edition
6
Turning Off the Calculator
To turn off the TI-83 Plus manually, press y M.
• All settings and memory contents are retained by Constant
MemoryTM.
• Any error condition is cleared.
Batteries
The TI-83 Plus uses four AAA alkaline batteries and has a user-
replaceable backup lithium battery (CR1616 or CR1620). To replace
batteries without losing any information stored in memory, follow the
steps in Appendix B.
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Operating the TI-83 Plus Silver Edition
7
Setting the Display Contrast
Adjusting the Display Contrast
You can adjust the display contrast to suit your viewing angle and lighting
conditions. As you change the contrast setting, a number from 0 (lightest)
to 9 (darkest) in the top-right corner indicates the current level. You may
not be able to see the number if contrast is too light or too dark.
Note: The TI-83 Plus has 40 contrast settings, so each number 0 through 9
represents four settings.
The TI-83 Plus retains the contrast setting in memory when it is turned
off.
To adjust the contrast, follow these steps.
1. Press and release the y key.
2. Press and hold † or }, which are below and above the contrast
symbol (yellow, half-shaded circle).
•
•
† lightens the screen.
} darkens the screen.
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Operating the TI-83 Plus Silver Edition
8
Note: If you adjust the contrast setting to 0, the display may become completely
blank. To restore the screen, press and release y, and then press and hold
} until the display reappears.
When to Replace Batteries
When the batteries are low, a low-battery message is displayed when
you:
• Turn on the calculator.
• Download a new application.
• Attempt to upgrade to new software.
To replace the batteries without losing any information in memory, follow
the steps in Appendix B.
Generally, the calculator will continue to operate for one or two weeks
after the low-battery message is first displayed. After this period, the
TI-83 Plus will turn off automatically and the unit will not operate.
Batteries must be replaced. All memory should be retained.
Note: The operating period following the first low-battery message could be
longer than two weeks if you use the calculator infrequently.
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Operating the TI-83 Plus Silver Edition
9
The Display
Types of Displays
The TI-83 Plus displays both text and graphs. Chapter 3 describes
graphs. Chapter 9 describes how the TI-83 Plus can display a
horizontally or vertically split screen to show graphs and text
simultaneously.
Home Screen
The home screen is the primary screen of the TI-83 Plus. On this screen,
enter instructions to execute and expressions to evaluate. The answers
are displayed on the same screen.
Displaying Entries and Answers
When text is displayed, the TI-83 Plus screen can display a maximum of
8 lines with a maximum of 16 characters per line. If all lines of the display
are full, text scrolls off the top of the display. If an expression on the
home screen, the Y= editor (Chapter 3), or the program editor
(Chapter 16) is longer than one line, it wraps to the beginning of the next
line. In numeric editors such as the window screen (Chapter 3), a long
expression scrolls to the right and left.
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Operating the TI-83 Plus Silver Edition
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When an entry is executed on the home screen, the answer is displayed
on the right side of the next line.
Entry
Answer
The mode settings control the way the TI-83 Plus interprets expressions
and displays answers.
If an answer, such as a list or matrix, is too long to display entirely on
one line, an ellipsis (...) is displayed to the right or left. Press ~ and | to
display the answer.
Entry
Answer
Returning to the Home Screen
To return to the home screen from any other screen, press y 5.
Busy Indicator
When the TI-83 Plus is calculating or graphing, a vertical moving line is
displayed as a busy indicator in the top-right corner of the screen. When
you pause a graph or a program, the busy indicator becomes a vertical
moving dotted line.
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Operating the TI-83 Plus Silver Edition
11
Display Cursors
In most cases, the appearance of the cursor indicates what will happen
when you press the next key or select the next menu item to be pasted
as a character.
Cursor
Appearance
Effect of Next Keystroke
Entry
Solid rectangle
$
A character is entered at the cursor; any
existing character is overwritten
Insert
Second
Alpha
Full
Underline
__
A character is inserted in front of the cursor
location
Reverse arrow
Þ
A 2nd character (yellow on the keyboard) is
entered or a 2nd operation is executed
Reverse A
Ø
An alpha character (green on the keyboard)
is entered or SOLVE is executed
Checkerboard
rectangle
#
No entry; the maximum characters are
entered at a prompt or memory is full
If you press ƒ during an insertion, the cursor becomes an underlined
A (A). If you press y during an insertion, the underlined cursor becomes
an underlined # (#).
Graphs and editors sometimes display additional cursors, which are
described in other chapters.
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Operating the TI-83 Plus Silver Edition
12
Entering Expressions and Instructions
What Is an Expression?
An expression is a group of numbers, variables, functions and their
arguments, or a combination of these elements. An expression evaluates
to a single answer. On the TI-83 Plus, you enter an expression in the
same order as you would write it on paper. For example, pR2 is an
expression.
You can use an expression on the home screen to calculate an answer.
In most places where a value is required, you can use an expression to
enter a value.
Entering an Expression
To create an expression, you enter numbers, variables, and functions
from the keyboard and menus. An expression is completed when you
press Í, regardless of the cursor location. The entire expression is
the answer is displayed.
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Operating the TI-83 Plus Silver Edition
13
Most TI-83 Plus functions and operations are symbols comprising
several characters. You must enter the symbol from the keyboard or a
menu; do not spell it out. For example, to calculate the log of 45, you
must press « 45. Do not enter the letters L, O, and G. If you enter LOG,
the TI-83 Plus interprets the entry as implied multiplication of the
variables L, O, and G.
Calculate 3.76 ÷ (L7.9 + ‡5) + 2 log 45.
3 Ë 76 ¥ £ Ì 7 Ë 9 Ã y C
5 ¤ ¤ Ã 2 « 45 ¤
Í
Multiple Entries on a Line
To enter two or more expressions or instructions on a line, separate
them with colons (ƒ [:]). All instructions are stored together in last
Entering a Number in Scientific Notation
To enter a number in scientific notation, follow these steps.
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Operating the TI-83 Plus Silver Edition
14
1. Enter the part of the number that precedes the exponent. This value
can be an expression.
2. Press y D. å is pasted to the cursor location.
3. If the exponent is negative, press Ì, and then enter the exponent,
which can be one or two digits.
When you enter a number in scientific notation, the TI-83 Plus does not
automatically display answers in scientific or engineering notation. The
Functions
A function returns a value. For example, ÷, L, +, ‡(, and log( are the
functions in the example on the previous page. In general, the first letter of
each function is lowercase on the TI-83 Plus. Most functions take at least
one argument, as indicated by an open parenthesis ( ( ) following the
name. For example, sin( requires one argument, sin(value).
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Operating the TI-83 Plus Silver Edition
15
Instructions
An instruction initiates an action. For example, ClrDraw is an instruction
that clears any drawn elements from a graph. Instructions cannot be
used in expressions. In general, the first letter of each instruction name
is uppercase. Some instructions take more than one argument, as
indicated by an open parenthesis ( ( ) at the end of the name. For
example, Circle( requires three arguments, Circle(X,Y,radius).
Interrupting a Calculation
To interrupt a calculation or graph in progress, which is indicated by the
busy indicator, press É.
When you interrupt a calculation, a menu is displayed.
• To return to the home screen, select 1:Quit.
• To go to the location of the interruption, select 2:Goto.
When you interrupt a graph, a partial graph is displayed.
• To return to the home screen, press ‘ or any nongraphing key.
• To restart graphing, press a graphing key or select a graphing
instruction.
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Operating the TI-83 Plus Silver Edition
16
TI-83 Plus Edit Keys
Keystrokes
~ or |
} or †
Result
Moves the cursor within an expression; these keys repeat.
Moves the cursor from line to line within an expression that
occupies more than one line; these keys repeat.
On the top line of an expression on the home screen, } moves
the cursor to the beginning of the expression.
On the bottom line of an expression on the home screen, †
moves the cursor to the end of the expression.
y |
y ~
Í
‘
Moves the cursor to the beginning of an expression.
Moves the cursor to the end of an expression.
Evaluates an expression or executes an instruction.
On a line with text on the home screen, clears the current line.
On a blank line on the home screen, clears everything on the
home screen.
In an editor, clears the expression or value where the cursor is
located; it does not store a zero.
{
Deletes a character at the cursor; this key repeats.
y 6
Changes the cursor to an underline (__); inserts characters in
front of the underline cursor; to end insertion, press y 6 or
press |, }, ~, or †.
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Operating the TI-83 Plus Silver Edition
17
Keystrokes
Result
y
Changes the cursor to Þ; the next keystroke performs a 2nd
operation (an operation in yellow above a key and to the left); to
cancel 2nd, press y again.
ƒ
Changes the cursor to Ø; the next keystroke pastes an alpha
character (a character in green above a key and to the right) or
executes SOLVE (Chapters 10 and 11); to cancel ƒ, press
ƒ or press |, }, ~, or †.
y 7
„
Changes the cursor to Ø; sets alpha-lock; subsequent
keystrokes (on an alpha key) paste alpha characters; to cancel
alpha-lock, press ƒ. If you are prompted to enter a name
such as for a group or a program, alpha-lock is set automatically.
Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or
an n in Seq mode with one keystroke.
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Operating the TI-83 Plus Silver Edition
18
Setting Modes
Checking Mode Settings
Mode settings control how the TI-83 Plus displays and interprets
numbers and graphs. Mode settings are retained by the Constant
Memory feature when the TI-83 Plus is turned off. All numbers, including
elements of matrices and lists, are displayed according to the current
mode settings.
To display the mode settings, press z. The current settings are
highlighted. Defaults are highlighted below. The following pages describe
the mode settings in detail.
Normal Sci Eng
Float 0123456789
Radian Degree
Numeric notation
Number of decimal places
Unit of angle measure
Func Par Pol Seq
Connected Dot
Sequential Simul
Real a+bi re^qi
Full Horiz G-T
Type of graphing
Whether to connect graph points
Whether to plot simultaneously
Real, rectangular complex, or polar complex
Full screen, two split-screen modes
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Operating the TI-83 Plus Silver Edition
19
Changing Mode Settings
To change mode settings, follow these steps.
1. Press † or } to move the cursor to the line of the setting that you
want to change.
2. Press ~ or | to move the cursor to the setting you want.
3. Press Í.
Setting a Mode from a Program
You can set a mode from a program by entering the name of the mode
as an instruction; for example, Func or Float. From a blank program
command line, select the mode setting from the mode screen; the
instruction is pasted to the cursor location.
Normal, Sci, Eng
Notation modes only affect the way an answer is displayed on the home
screen. Numeric answers can be displayed with up to 10 digits and a
two-digit exponent. You can enter a number in any format.
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Operating the TI-83 Plus Silver Edition
20
Normal notation mode is the usual way we express numbers, with digits
to the left and right of the decimal, as in 12345.67.
Sci (scientific) notation mode expresses numbers in two parts. The
significant digits display with one digit to the left of the decimal. The
appropriate power of 10 displays to the right of E, as in 1.234567E4.
Eng (engineering) notation mode is similar to scientific notation.
However, the number can have one, two, or three digits before the
decimal; and the power-of-10 exponent is a multiple of three, as in
12.34567E3.
Note: If you select Normal notation, but the answer cannot display in 10 digits
(or the absolute value is less than .001), the TI-83 Plus expresses the answer in
scientific notation.
Float, 0123456789
Float (floating) decimal mode displays up to 10 digits, plus the sign and
decimal.
0123456789 (fixed) decimal mode specifies the number of digits (0
through 9) to display to the right of the decimal. Place the cursor on the
desired number of decimal digits, and then press Í.
The decimal setting applies to Normal, Sci, and Eng notation modes.
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Operating the TI-83 Plus Silver Edition
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The decimal setting applies to these numbers:
• An answer displayed on the home screen
• Coordinates on a graph (Chapters 3, 4, 5, and 6)
• The Tangent( DRAW instruction equation of the line, x, and dy/dx
values (Chapter 8)
• Results of CALCULATE operations (Chapters 3, 4, 5, and 6)
• The regression equation stored after the execution of a regression
model (Chapter 12)
Radian, Degree
Angle modes control how the TI-83 Plus interprets angle values in
trigonometric functions and polar/rectangular conversions.
Radian mode interprets angle values as radians. Answers display in
radians.
Degree mode interprets angle values as degrees. Answers display in
degrees.
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Operating the TI-83 Plus Silver Edition
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Func, Par, Pol, Seq
Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6
describe these modes in detail.
Func (function) graphing mode plots functions, where Y is a function of X
(Chapter 3).
Par (parametric) graphing mode plots relations, where X and Y are
functions of T (Chapter 4).
Pol (polar) graphing mode plots functions, where r is a function of q
(Chapter 5).
Seq (sequence) graphing mode plots sequences (Chapter 6).
Connected, Dot
Connected plotting mode draws a line connecting each point calculated
for the selected functions.
Dot plotting mode plots only the calculated points of the selected
functions.
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Operating the TI-83 Plus Silver Edition
23
Sequential, Simul
Sequential graphing-order mode evaluates and plots one function
completely before the next function is evaluated and plotted.
Simul (simultaneous) graphing-order mode evaluates and plots all
selected functions for a single value of X and then evaluates and plots
them for the next value of X.
Note: Regardless of which graphing mode is selected, the TI-83 Plus will
sequentially graph all stat plots before it graphs any functions.
Real, a+bi, re^qi
Real mode does not display complex results unless complex numbers
are entered as input.
Two complex modes display complex results.
•
•
a+bi (rectangular complex mode) displays complex numbers in the
form a+bi.
re^qi (polar complex mode) displays complex numbers in the form
re^qi.
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Operating the TI-83 Plus Silver Edition
24
Full, Horiz, G.T
Full screen mode uses the entire screen to display a graph or edit
screen.
Each split-screen mode displays two screens simultaneously.
•
Horiz (horizontal) mode displays the current graph on the top half of
the screen; it displays the home screen or an editor on the bottom
half (Chapter 9).
•
G.T (graph-table) mode displays the current graph on the left half of
the screen; it displays the table screen on the right half (Chapter 9).
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Operating the TI-83 Plus Silver Edition
25
Using TI-83 Plus Variable Names
Variables and Defined Items
On the TI-83 Plus you can enter and use several types of data, including
real and complex numbers, matrices, lists, functions, stat plots, graph
databases, graph pictures, and strings.
The TI-83 Plus uses assigned names for variables and other items
saved in memory. For lists, you also can create your own five-character
names.
Variable Type
Names
Real numbers
Complex numbers
Matrices
A, B, ... , Z
A, B, ... , Z
ãAä, ãBä, ãCä, ... , ãJä
L1, L2, L3, L4, L5, L6, and user-defined names
Y1, Y2, . . . , Y9, Y0
X1T and Y1T, . . . , X6T and Y6T
r1, r2, r3, r4, r5, r6
Lists
Functions
Parametric equations
Polar functions
Sequence functions
Stat plots
u, v, w
Plot1, Plot2, Plot3
GDB1, GDB2, . . . , GDB9, GDB0
Graph databases
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Operating the TI-83 Plus Silver Edition
26
Variable Type
Graph pictures
Strings
Names
Pic1, Pic2, ... , Pic9, Pic0
Str1, Str2, ... , Str9, Str0
Applications
Apps
AppVars
Application variables
Grouped variables
Xmin, Xmax, and others
Groups
System variables
Notes about Variables
• You can create as many list names as memory will allow
(Chapter 11).
• Programs have user-defined names and share memory with
variables (Chapter 16).
• From the home screen or from a program, you can store to matrices
(Chapter 10), lists (Chapter 11), strings (Chapter 15), system
variables such as Xmax (Chapter 1), TblStart (Chapter 7), and all Y=
functions (Chapters 3, 4, 5, and 6).
• From an editor, you can store to matrices, lists, and Y= functions
(Chapter 3).
• From the home screen, a program, or an editor, you can store a
value to a matrix element or a list element.
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Operating the TI-83 Plus Silver Edition
27
• You can use DRAW STO menu items to store and recall graph
databases and pictures (Chapter 8).
• Although most variables can be archived, system variables including
r, t, x, y, and q cannot be archived (Chapter 18)
•
Apps are independent applications.which are stored in Flash ROM.
AppVars is a variable holder used to store variables created by
independent applications. You cannot edit or change variables in
AppVars unless you do so through the application which created
them.
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Operating the TI-83 Plus Silver Edition
28
Storing Variable Values
Storing Values in a Variable
Values are stored to and recalled from memory using variable names.
When an expression containing the name of a variable is evaluated, the
value of the variable at that time is used.
To store a value to a variable from the home screen or a program using
the ¿ key, begin on a blank line and follow these steps.
1. Enter the value you want to store. The value can be an expression.
2. Press ¿. ! is copied to the cursor location.
3. Press ƒ and then the letter of the variable to which you want to
store the value.
4. Press Í. If you entered an expression, it is evaluated. The value
is stored to the variable.
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Operating the TI-83 Plus Silver Edition
29
Displaying a Variable Value
To display the value of a variable, enter the name on a blank line on the
home screen, and then press Í.
Archiving Variables (Archive, Unarchive)
You can archive data, programs, or other variables in a section of
memory called user data archive where they cannot be edited or deleted
inadvertently. Archived variables are indicated by asterisks (*) to the left
of the variable names. Archived variables cannot be edited or executed.
They can only be seen and unarchived. For example, if you archive list
L1, you will see that L1 exists in memory but if you select it and paste the
name L1 to the home screen, you won’t be able to see its contents or
edit it until they are unarchived.
.
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Operating the TI-83 Plus Silver Edition
30
Recalling Variable Values
Using Recall (RCL)
To recall and copy variable contents to the current cursor location, follow
these steps. To leave RCL, press ‘.
1. Press y ãRCLä. RCL and the edit cursor are displayed on the bottom
line of the screen.
2. Enter the name of the variable in any of five ways.
• Press ƒ and then the letter of the variable.
• Press y ãLISTä, and then select the name of the list, or press y
[Ln].
• Press y >, and then select the name of the matrix.
• Press to display the VARS menu or ~ to display the
VARS Y.VARS menu; then select the type and then the name of the
variable or function.
• Press |, and then select the name of the program (in the
program editor only).
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Operating the TI-83 Plus Silver Edition
31
The variable name you selected is displayed on the bottom line and
the cursor disappears.
3. Press Í. The variable contents are inserted where the cursor
was located before you began these steps.
Note: You can edit the characters pasted to the expression without
affecting the value in memory.
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Operating the TI-83 Plus Silver Edition
32
ENTRY (Last Entry) Storage Area
Using ENTRY (Last Entry)
When you press Í on the home screen to evaluate an expression or
execute an instruction, the expression or instruction is placed in a
storage area called ENTRY (last entry). When you turn off the TI-83 Plus,
ENTRY is retained in memory.
To recall ENTRY, press y [. The last entry is pasted to the current
cursor location, where you can edit and execute it. On the home screen
or in an editor, the current line is cleared and the last entry is pasted to
the line.
Because the TI-83 Plus updates ENTRY only when you press Í, you
can recall the previous entry even if you have begun to enter the next
expression.
5 Ã 7
Í
y [
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Operating the TI-83 Plus Silver Edition
33
Accessing a Previous Entry
The TI-83 Plus retains as many previous entries as possible in ENTRY, up
to a capacity of 128 bytes. To scroll those entries, press y [
repeatedly. If a single entry is more than 128 bytes, it is retained for
ENTRY, but it cannot be placed in the ENTRY storage area.
1 ¿ ƒ A
Í
2 ¿ ƒ B
Í
y [
If you press y [ after displaying the oldest stored entry, the
newest stored entry is displayed again, then the next-newest entry, and
so on.
y [
Reexecuting the Previous Entry
After you have pasted the last entry to the home screen and edited it (if
you chose to edit it), you can execute the entry. To execute the last
entry, press Í.
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Operating the TI-83 Plus Silver Edition
34
To reexecute the displayed entry, press Í again. Each reexecution
displays an answer on the right side of the next line; the entry itself is not
redisplayed.
0 ¿ ƒ N
Í
ƒ N Ã 1 ¿ ƒ N ƒ
ã:ä ƒ N ¡ Í
Í
Í
Multiple Entry Values on a Line
To store to ENTRY two or more expressions or instructions, separate each
expression or instruction with a colon, then press Í. All expressions
and instructions separated by colons are stored in ENTRY.
When you press y [, all the expressions and instructions separated
by colons are pasted to the current cursor location. You can edit any of the
entries, and then execute all of them when you press Í.
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Operating the TI-83 Plus Silver Edition
35
2
For the equation A=pr , use trial and error to find the radius of a circle that covers 200
square centimeters. Use 8 as your first guess.
8 ¿ ƒ R ƒ [:] y B
ƒ R ¡ Í y [
y | 7 y 6 Ë 95
Í
Continue until the answer is as accurate as you want.
Clearing ENTRY
Clear Entries (Chapter 18) clears all data that the TI-83 Plus is holding in
the ENTRY storage area.
Using Ans in an Expression
When an expression is evaluated successfully from the home screen or
from a program, the TI-83 Plus stores the answer to a storage area
called Ans (last answer). Ans may be a real or complex number, a list, a
matrix, or a string. When you turn off the TI-83 Plus, the value in Ans is
retained in memory.
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Operating the TI-83 Plus Silver Edition
36
You can use the variable Ans to represent the last answer in most places.
Press y Z to copy the variable name Ans to the cursor location. When
the expression is evaluated, the TI-83 Plus uses the value of Ans in the
calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield
per square meter if the plot produces a total of 147 tomatoes.
1 Ë 7 ¯ 4 Ë 2
Í
147 ¥ y Z
Í
Continuing an Expression
You can use Ans as the first entry in the next expression without entering
the value again or pressing y Z. On a blank line on the home
screen, enter the function. The TI-83 Plus pastes the variable name Ans
to the screen, then the function.
5 ¥ 2
Í
¯ 9 Ë 9
Í
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Operating the TI-83 Plus Silver Edition
37
Storing Answers
To store an answer, store Ans to a variable before you evaluate another
expression.
Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder
of radius 5 meters and height 3.3 meters, and then store the result in the variable V.
y B 5 ¡
Í
¯ 3 Ë 3
Í
¿ ƒ V
Í
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Operating the TI-83 Plus Silver Edition
38
TI-83 Plus Menus
Using a TI-83 Plus Menu
You can access most TI-83 Plus operations using menus. When you
press a key or key combination to display a menu, one or more menu
names appear on the top line of the screen.
• The menu name on the left side of the top line is highlighted. Up to
seven items in that menu are displayed, beginning with item 1, which
also is highlighted.
• A number or letter identifies each menu item’s place in the menu. The
order is 1 through 9, then 0, then A, B, C, and so on. The LIST NAMES,
PRGM EXEC, and PRGM EDIT menus only label items 1 through 9 and 0.
• When the menu continues beyond the displayed items, a down arrow
($) replaces the colon next to the last displayed item.
• When a menu item ends in an ellipsis (...), the item displays a
secondary menu or editor when you select it.
• When an asterisk (*) appears to the left of a menu item, that item is
stored in user data archive (Chapter 18).
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Operating the TI-83 Plus Silver Edition
39
To display any other menu listed on the top line, press ~ or | until that
menu name is highlighted. The cursor location within the initial menu is
irrelevant. The menu is displayed with the cursor on the first item.
Note: The Menu Map in Appendix A shows each menu, each operation under
each menu, and the key or key combination you press to display each menu.
Displaying a Menu
While using your TI-83 Plus, you often will need
to access items from its menus.
When you press a key that displays a menu, that
menu temporarily replaces the screen where you
are working. For example, when you press ,
the MATH menu is displayed as a full screen.
After you select an item from a menu, the screen
where you are working usually is displayed again.
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Operating the TI-83 Plus Silver Edition
40
Moving from One Menu to Another
Some keys access more than one menu. When
you press such a key, the names of all accessible
menus are displayed on the top line. When you
highlight a menu name, the items in that menu are
displayed. Press ~ and | to highlight each menu
name.
Scrolling a Menu
To scroll down the menu items, press †. To scroll up the menu items,
press }.
To page down six menu items at a time, press ƒ †. To page up six
menu items at a time, press ƒ }. The green arrows on the
calculator, between † and }, are the page-down and page-up symbols.
To wrap to the last menu item directly from the first menu item, press }.
To wrap to the first menu item directly from the last menu item, press †.
Selecting an Item from a Menu
You can select an item from a menu in either of two ways.
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41
• Press the number or letter of the item you want
to select. The cursor can be anywhere on the
menu, and the item you select need not be
displayed on the screen.
• Press † or } to move the cursor to the item
you want, and then press Í.
After you select an item from a menu, the
TI-83 Plus typically displays the previous screen.
Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1
through 9 and 0 are labeled in such a way that you can select them by pressing
the appropriate number key. To move the cursor to the first item beginning with
any alpha character or q, press the key combination for that alpha character or
q. If no items begin with that character, the cursor moves beyond it to the next
item.
3
Calculate ‡27.
† † † Í
27 ¤ Í
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Operating the TI-83 Plus Silver Edition
42
Leaving a Menu without Making a Selection
You can leave a menu without making a selection in any of four ways.
• Press y 5 to return to the home screen.
• Press ‘ to return to the previous screen.
• Press a key or key combination for a different menu, such as or
y 9.
• Press a key or key combination for a different screen, such as o or
y 0.
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43
VARS and VARS Y.VARS Menus
VARS Menu
You can enter the names of functions and system variables in an
expression or store to them directly.
To display the VARS menu, press . All VARS menu items display
secondary menus, which show the names of the system variables.
1:Window, 2:Zoom, and 5:Statistics each access more than one
secondary menu.
VARS Y-VARS
1:Window...
X/Y, T/q, and U/V/W variables
ZX/ZY, ZT/Zq, and ZU variables
Graph database variables
Picture variables
XY, G, EQ, TEST, and PTS variables
TABLE variables
2:Zoom...
3:GDB...
4:Picture...
5:Statistics...
6:Table...
7:String...
String variables
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44
Selecting a Variable from the VARS Menu or VARS Y.VARS Menu
To display the VARS Y.VARS menu, press ~. 1:Function,
2:Parametric, and 3:Polar display secondary menus of the Y= function
variables.
VARS Y-VARS
1:Function...
2:Parametric...
3:Polar...
Yn functions
XnT, YnT functions
rn functions
4:On/Off...
Lets you select/deselect functions
Note: The sequence variables (u, v, w) are located on the keyboard as the
second functions of ¬, −, and ®.
To select a variable from the VARS or VARS Y.VARS menu, follow these
steps.
1. Display the VARS or VARS Y.VARS menu.
• Press to display the VARS menu.
• Press ~ to display the VARS Y.VARS menu.
2. Select the type of variable, such as 2:Zoom from the VARS menu or
3:Polar from the VARS Y.VARS menu. A secondary menu is displayed.
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45
3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu,
you can press ~ or | to display other secondary menus.
4. Select a variable name from the menu. It is pasted to the cursor
location.
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Operating the TI-83 Plus Silver Edition
46
Equation Operating System (EOS)
Order of Evaluation
The Equation Operating System (EOS) defines the order in which
functions in expressions are entered and evaluated on the TI-83 Plus.
EOS lets you enter numbers and functions in a simple, straightforward
sequence.
EOS evaluates the functions in an expression in this order.
Order Number Function
Functions that precede the argument, such as ‡(, sin(, or log(
1
2
2 M1
Functions that are entered after the argument, such as , , !, ¡,
r
, and conversions
x
Powers and roots, such as 2^5 or 5 ‡32
3
4
5
6
7
8
9
Permutations (nPr) and combinations (nCr)
Multiplication, implied multiplication, and division
Addition and subtraction
Relational functions, such as > or
Logic operator and
Logic operators or and xor
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47
Note: Within a priority level, EOS evaluates functions from left to right.
Calculations within parentheses are evaluated first.
Implied Multiplication
The TI-83 Plus recognizes implied multiplication, so you need not press
¯ to express multiplication in all cases. For example, the TI-83 Plus
interprets 2p, 4sin(46), 5(1+2), and (2ä5)7 as implied multiplication.
Note: TI-83 Plus implied multiplication rules, although like theTI.83, differ from
those of the TI.82. For example, the TI-83 Plus evaluates 1à2X as (1à2)äX,
while the TI.82 evaluates 1à2X as 1/(2äX) (Chapter 2).
Parentheses
All calculations inside a pair of parentheses are completed first. For
example, in the expression 4(1+2), EOS first evaluates the portion inside
the parentheses, 1+2, and then multiplies the answer, 3, by 4.
You can omit the close parenthesis ( ) ) at the end of an expression. All
open parenthetical elements are closed automatically at the end of an
expression. This is also true for open parenthetical elements that
precede the store or display-conversion instructions.
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48
Note: An open parenthesis following a list name, matrix name, or Y= function
name does not indicate implied multiplication. It specifies elements in the list
(Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the
Y= function.
Negation
To enter a negative number, use the negation key. Press Ì and then
enter the number. On the TI-83 Plus, negation is in the third level in the
EOS hierarchy. Functions in the first level, such as squaring, are
evaluated before negation.
2
For example, MX , evaluates to a negative number (or 0). Use
parentheses to square a negative number.
Note: Use the ¹ key for subtraction and the Ì key for negation. If you press ¹
to enter a negative number, as in 9 ¯ ¹ 7, or if you press Ì to indicate
subtraction, as in 9 Ì 7, an error occurs. If you press ƒ A Ì ƒ B, it is
interpreted as implied multiplication (AäMB).
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Operating the TI-83 Plus Silver Edition
49
Special Features of the TI-83 Plus
Flash – Electronic Upgradability
The TI-83 Plus uses Flash
technology, which lets you
upgrade to future software
versions without buying a new
calculator.
For details, refer to:
Chapter 19
As new functionality becomes available, you can electronically upgrade
your TI-83 Plus from the Internet. Future software versions include
maintenance upgrades that will be released free of charge, as well as
new applications and major software upgrades that will be available for
1.56 Megabytes (M) of Available Memory
1.56 M of available memory are built into the
TI-83 Plus. About 24 kilobytes (K) of RAM
(random access memory) are available for you
to compute and store functions, programs, and
data.
For details, refer to:
Chapter 18
About 1.54 M of user data archive allow you to store data, programs,
applications, or any other variables to a safe location where they cannot
TI-83 Plus
Operating the TI-83 Plus Silver Edition
50
be edited or deleted inadvertently. You can also free up RAM by
archiving variables to user data
Applications
Applications can be installed to customize the
TI-83 Plus to your classroom needs. The big
1.54 M archive space lets you store up to 94
applications at one time. Applications can also
be stored on a computer for later use or linked
unit-to-unit.
For details, refer to:
Chapter 18
Archiving
You can store variables in the TI-83 Plus user
data archive, a protected area of memory
separate from RAM. The user data archive lets
you:
For details, refer to:
Chapter 18
• Store data, programs, applications or any other variables to a safe
location where they cannot be edited or deleted inadvertently.
• Create additional free RAM by archiving variables.
By archiving variables that do not need to be edited frequently, you can
free up RAM for applications that may require additional memory.
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51
Calculator-Based Laboratoryé (CBL 2é, CBLé) and
Calculator-Based Rangeré (CBRé)
The TI-83 Plus comes with the CBL/CBR
application already installed. When coupled
with the (optional) CBL 2/CBL or CBR
accessories, you can use the TI-83 Plus to
analyze real world data.
For details, refer to:
Chapter 14
CBL 2/CBL and CBR let you explore mathematical and scientific
relationships among distance, velocity, acceleration, and time using data
collected from activities you perform.
CBL 2/CBL and CBR differ in that CBL 2/CBL allows you to collect data
using several different probes analyzing temperature, light, voltage, or
sonic (motion) data. CBR collects data using a built-in Sonic probe.
CBL 2/CBL and CBR accessories can be linked together to collect more
than one type of data at the same time. You can find more information
TI-83 Plus
Operating the TI-83 Plus Silver Edition
52
Other TI-83 Plus Features
Getting Started has introduced you to basic TI-83 Plus operations. This
guidebook covers the other features and capabilities of the TI-83 Plus in
greater detail.
Graphing
You can store, graph, and analyze up to 10
functions, up to six parametric functions, up to
six polar functions, and up to three sequences.
You can use DRAW instructions to annotate
graphs.
For graphing details,
refer to:
Chapters 3, 4, 5, 6, 8
The graphing chapters appear in this order: Function, Parametric, Polar,
Sequence, and DRAW.
Sequences
You can generate sequences and graph them
over time. Or, you can graph them as web plots
or as phase plots.
For details, refer to:
Chapter 6
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Operating the TI-83 Plus Silver Edition
53
Tables
You can create function evaluation tables to
analyze many functions simultaneously.
For details, refer to:
Chapter 7
Split Screen
You can split the screen horizontally to display
both a graph and a related editor (such as the
Y= editor), the table, the stat list editor, or the
home screen. Also, you can split the screen
vertically to display a graph and its table
simultaneously.
For details, refer to:
Chapter 9
Matrices
You can enter and save up to 10 matrices and
perform standard matrix operations on them.
For details, refer to:
Chapter 10
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54
Lists
You can enter and save as many lists as
memory allows for use in statistical analyses.
You can attach formulas to lists for automatic
computation. You can use lists to evaluate
expressions at multiple values simultaneously
and to graph a family of curves.
For details, refer to:
Chapter 11
Statistics
You can perform one- and two-variable, list-
based statistical analyses, including logistic and
sine regression analysis. You can plot the data
as a histogram, xyLine, scatter plot, modified or
regular box-and-whisker plot, or normal
probability plot. You can define and store up to
three stat plot definitions.
For details, refer to:
Chapter 12
Inferential Statistics
You can perform 16 hypothesis tests and
confidence intervals and 15 distribution
functions. You can display hypothesis test
results graphically or numerically.
For details, refer to:
Chapter 13
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55
Applications
You can use such applications as Finance or
the CBL/CBR. With the Finance application you
can use time-value-of-money (TVM) functions to
analyze financial instruments such as annuities,
For details, refer to:
Chapter 14
loans, mortgages, leases, and savings. You can analyze the value of
money over equal time periods using cash flow functions. You can
amortize loans with the amortization functions. With the CBL/CBR
applications and CBL 2/CBL or CBR (optional) accessories, you can use
a variety of probes to collect real world data.
Your TI-83 Plus includes Flash applications in addition to the ones
mentioned above. Press Πto see the complete list of applications
that came with your calculator.
Documentation for TI Flash applications is on the TI Resource CD. Visit
CATALOG
The CATALOG is a convenient, alphabetical list of
all functions and instructions on the TI-83 Plus.
You can paste any function or instruction from
the CATALOG to the current cursor location.
For details, refer to:
Chapter 15
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56
Programming
You can enter and store programs that include
extensive control and input/output instructions.
For details, refer to:
Chapter 16
Archiving
Archiving allows you to store data, programs, or
other variables to user data archive where they
cannot be edited or deleted inadvertently.
Archiving also allows you to free up RAM for
variables that may require additional memory.
For details, refer to:
Chapter 16
Archived variables are
indicated by asterisks (*) to
the left of the variable
names.
Communication Link
The TI-83 Plus has a port to connect and
communicate with another TI-83 Plus, a
TI-83 Plus, a TI.83, a TI-82, a TI-73,
CBL 2/CBL, or a CBR System.
For details, refer to:
Chapter 19
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Operating the TI-83 Plus Silver Edition
57
With the TI™ Connect or TI-GRAPH LINK™ software and a TI-GRAPH LINK
cable, you can also link the TI-83 Plus to a personal computer.
As future software upgrades become available on the TI web site, you
can download the software to your PC and then use the TI Connect or
TI-GRAPH LINK software and a TI-GRAPH LINK cable to upgrade your
TI-83 Plus.
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Operating the TI-83 Plus Silver Edition
58
Error Conditions
Diagnosing an Error
The TI-83 Plus detects errors while performing these tasks.
• Evaluating an expression
• Executing an instruction
• Plotting a graph
• Storing a value
When the TI-83 Plus detects an error, it returns an error message as a
menu title, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes
each error type and possible reasons for the error.
• If you select 1:Quit (or press y 5 or ‘), then the home
screen is displayed.
• If you select 2:Goto, then the previous screen is displayed with the
cursor at or near the error location.
Note: If a syntax error occurs in the contents of a Y= function during program
execution, then the Goto option returns to the Y= editor, not to the program.
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59
Correcting an Error
To correct an error, follow these steps.
1. Note the error type (ERR:error type).
2. Select 2:Goto, if it is available. The previous screen is displayed with
the cursor at or near the error location.
3. Determine the error. If you cannot recognize the error, refer to
Appendix B.
4. Correct the expression.
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60
Chapter 2:
Math, Angle, and Test Operations
Getting Started: Coin Flip
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to model flipping a fair coin 10 times. You want to track how
many of those 10 coin flips result in heads. You want to perform this simulation
40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5
and the probability of a coin flip resulting in tails is 0.5.
1. Begin on the home screen. Press | to
display the MATH PRB menu. Press 7 to select
7:randBin( (random Binomial). randBin( is pasted
to the home screen. Press 10 to enter the
number of coin flips. Press ¢. Press Ë 5 to
enter the probability of heads. Press ¢. Press
40 to enter the number of simulations. Press ¤.
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61
2. Press Í to evaluate the expression. A list of
40 elements is generated with the first 7
displayed. The list contains the count of heads
resulting from each set of 10 coin flips. The list
has 40 elements because this simulation was
performed 40 times. In this example, the coin
came up heads five times in the first set of 10
coin flips, five times in the second set of 10 coin
flips, and so on.
3. Press ~ or | to view the additional counts in
the list. Ellipses (...) indicate that the list
continues beyond the screen.
4. Press ¿ y ãL1ä Í to store the data to
the list name L1. You then can use the data for
another activity, such as plotting a histogram
(Chapter 12).
Note: Since randBin( generates random numbers,
your list elements may differ from those in the
example.
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62
Keyboard Math Operations
Using Lists with Math Operations
Math operations that are valid for lists return a list calculated element by
element. If you use two lists in the same expression, they must be the
same length.
+ (Addition), N (Subtraction), ä (Multiplication), à (Division)
You can use + (addition, Ã), N (subtraction, ¹), ä (multiplication, ¯), and
à (division, ¥) with real and complex numbers, expressions, lists, and
matrices. You cannot use à with matrices.
valueA+valueB
valueA N valueB
valueAävalueB
valueA à valueB
Trigonometric Functions
You can use the trigonometric (trig) functions (sine, ˜; cosine, ™;
and tangent, š) with real numbers, expressions, and lists. The current
angle mode setting affects interpretation. For example, sin(30) in Radian
mode returns L.9880316241; in Degree mode it returns .5.
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63
sin(value)
cos(value)
tan(value)
You can use the inverse trig functions (arcsine, y ?; arccosine, y
@; and arctangent, y A) with real numbers, expressions, and
lists. The current angle mode setting affects interpretation.
L1
L1
L1
sin (value)
cos (value)
tan (value)
Note: The trig functions do not operate on complex numbers.
^ (Power), 2 (Square), ‡( (Square Root)
You can use ^ (power, ›), 2 (square, ¡), and ‡( (square root, y C)
with real and complex numbers, expressions, lists, and matrices. You
cannot use ‡( with matrices.
2
value^power
value
‡(value)
1 (Inverse)
L
You can use L1 (inverse, œ) with real and complex numbers,
expressions, lists, and matrices. The multiplicative inverse is equivalent
to the reciprocal, 1àx.
L1
value
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64
log(, 10^(, ln(
You can use log( (logarithm, «), 10^( (power of 10, y G), and ln(
(natural log, µ) with real or complex numbers, expressions, and lists.
log(value)
10^(power)
ln(value)
e^( (Exponential)
e^( (exponential, y J) returns the constant e raised to a power. You
can use e^( with real or complex numbers, expressions, and lists.
e^(power)
e (Constant)
e (constant, y [e]) is stored as a constant on the TI-83 Plus. Press
y [e] to copy e to the cursor location. In calculations, the TI-83 Plus
uses 2.718281828459 for e.
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65
L (Negation)
M (negation, Ì) returns the negative of value. You can use M with real or
complex numbers, expressions, lists, and matrices.
Mvalue
EOS™ rules (Chapter 1) determine when negation is evaluated. For
2
example, LA returns a negative number, because squaring is evaluated
before negation. Use parentheses to square a negated number, as in
2
(LA) .
Note: On the TI-83 Plus, the negation symbol (M) is shorter and higher than the
subtraction sign (N), which is displayed when you press ¹.
p (Pi)
p (Pi, y B) is stored as a constant in the TI-83 Plus. In calculations,
the TI-83 Plus uses 3.1415926535898 for p.
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66
MATH Operations
MATH Menu
To display the MATH menu, press .
MATH NUM CPX PRB
1:4Frac
Displays the answer as a fraction.
Displays the answer as a decimal.
Calculates the cube.
Calculates the cube root.
Calculates the xth root.
2:4Dec
3
3:
3
4: ‡(
x
5:
‡
6:fMin(
Finds the minimum of a function.
Finds the maximum of a function.
Computes the numerical derivative.
Computes the function integral.
Displays the equation solver.
7:fMax(
8:nDeriv(
9:fnInt(
0:Solver...
4Frac, 4Dec
4Frac (display as a fraction) displays an answer as its rational equivalent.
You can use 4Frac with real or complex numbers, expressions, lists, and
matrices. If the answer cannot be simplified or the resulting denominator
is more than three digits, the decimal equivalent is returned. You can
only use 4Frac following value.
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67
value 4Frac
4Dec (display as a decimal) displays an answer in decimal form. You can
use 4Dec with real or complex numbers, expressions, lists, and matrices.
You can only use 4Dec following value.
value 4Dec
3(Cube), 3‡( (Cube Root)
3 (cube) returns the cube of value. You can use 3 with real or complex
numbers, expressions, lists, and square matrices.
value3
‡( (cube root) returns the cube root of value. You can use 3‡( with real or
3
complex numbers, expressions, and lists.
3
‡(value)
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68
x
x
‡ (Root)
‡ (xth root) returns the xth root of value. You can use x‡ with real or
complex numbers, expressions, and lists.
x
xthroot ‡value
fMin(, fMax(
fMin( (function minimum) and fMax( (function maximum) return the value
at which the local minimum or local maximum value of expression with
respect to variable occurs, between lower and upper values for variable.
fMin( and fMax( are not valid in expression. The accuracy is controlled by
tolerance (if not specified, the default is 1âL5).
fMin(expression,variable,lower,upper[,tolerance])
fMax(expression,variable,lower,upper[,tolerance])
Note: In this guidebook, optional arguments and the commas that accompany
them are enclosed in brackets ([ ]).
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nDeriv(
nDeriv( (numerical derivative) returns an approximate derivative of
expression with respect to variable, given the value at which to calculate the
derivative and H (if not specified, the default is 1âL3). nDeriv( is valid only
for real numbers.
nDeriv(expression,variable,value[,H])
nDeriv( uses the symmetric difference quotient method, which
approximates the numerical derivative value as the slope of the secant
line through these points.
f (x +ε) − ( f (x −ε)
f '(x) =
2ε
As H becomes smaller, the approximation usually becomes more
accurate.
You can use nDeriv( once in expression. Because of the method used to
calculate nDeriv(, the TI-83 Plus can return a false derivative value at a
nondifferentiable point.
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70
fnInt(
fnInt( (function integral) returns the numerical integral (Gauss-Kronrod
method) of expression with respect to variable, given lower limit, upper limit,
and a tolerance (if not specified, the default is 1âL5). fnInt( is valid only for
real numbers.
fnInt(expression,variable,lower,upper[,tolerance])
Tip: To speed the drawing of integration graphs (when fnInt( is used in a Y=
equation), increase the value of the Xres window variable before you press
s.
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71
Using the Equation Solver
Solver
Solver displays the equation solver, in which you can solve for any
variable in an equation. The equation is assumed to be equal to zero.
Solver is valid only for real numbers.
When you select Solver, one of two screens is displayed.
• The equation editor (see step 1 picture below) is displayed when the
equation variable eqn is empty.
• The interactive solver editor is displayed when an equation is stored
in eqn.
Entering an Expression in the Equation Solver
To enter an expression in the equation solver, assuming that the variable
eqn is empty, follow these steps.
1. Select 0:Solver from the MATH menu to display the equation editor.
2. Enter the expression in any of three ways.
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72
• Enter the expression directly into the equation solver.
• Paste a Y= variable name from the VARS Y.VARS menu to the
equation solver.
• Press y K, paste a Y= variable name from the VARS Y.VARS
menu, and press Í. The expression is pasted to the equation
solver.
The expression is stored to the variable eqn as you enter it.
3. Press Í or †. The interactive solver editor is displayed.
• The equation stored in eqn is set equal to zero and displayed on
the top line.
• Variables in the equation are listed in the order in which they
appear in the equation. Any values stored to the listed variables
also are displayed.
• The default lower and upper bounds appear in the last line of the
editor (bound={L1å99,1å99}).
TI-83 Plus
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73
• A $ is displayed in the first column of the bottom line if the editor
continues beyond the screen.
2
Tip: To use the solver to solve an equation such as K=.5MV , enter
2
eqn:0=KN.5MV in the equation editor.
Entering and Editing Variable Values
When you enter or edit a value for a variable in the interactive solver
editor, the new value is stored in memory to that variable.
You can enter an expression for a variable value. It is evaluated when
you move to the next variable. Expressions must resolve to real numbers
at each step during the iteration.
You can store equations to any VARS Y.VARS variables, such as Y1 or r6,
and then reference the variables in the equation. The interactive solver
editor displays all variables of all Y= functions referenced in the equation.
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74
Solving for a Variable in the Equation Solver
To solve for a variable using the equation solver after an equation has
been stored to eqn, follow these steps.
1. Select 0:Solver from the MATH menu to display the interactive solver
editor, if not already displayed.
2. Enter or edit the value of each known variable. All variables, except
the unknown variable, must contain a value. To move the cursor to
the next variable, press Í or †.
3. Enter an initial guess for the variable for which you are solving. This
is optional, but it may help find the solution more quickly. Also, for
equations with multiple roots, the TI-83 Plus will attempt to display
the solution that is closest to your guess.
TI-83 Plus
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75
(upper+lower)
The default guess is calculated as
.
2
4. Edit bound={lower,upper}. lower and upper are the bounds between which
the TI-83 Plus searches for a solution. This is optional, but it may help
find the solution more quickly. The default is bound={L1å99,1å99}.
5. Move the cursor to the variable for which you want to solve and press
ƒ \ (above the Í key).
• The solution is displayed next to the variable for which you solved.
A solid square in the first column marks the variable for which you
solved and indicates that the equation is balanced. An ellipsis
shows that the value continues beyond the screen.
Note: When a number continues beyond the screen, be sure to press ~
to scroll to the end of the number to see whether it ends with a negative
or positive exponent. A very small number may appear to be a large
number until you scroll right to see the exponent.
• The values of the variables are updated in memory.
TI-83 Plus
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76
•
leftNrt=diff is displayed in the last line of the editor. diff is the
difference between the left and right sides of the equation. A solid
square in the first column next to leftNrt= indicates that the
equation has been evaluated at the new value of the variable for
which you solved.
Editing an Equation Stored to eqn
To edit or replace an equation stored to eqn when the interactive
equation solver is displayed, press } until the equation editor is
displayed. Then edit the equation.
Equations with Multiple Roots
Some equations have more than one solution. You can enter a new
initial guess or new bounds to look for additional solutions.
Further Solutions
After you solve for a variable, you can continue to explore solutions from
the interactive solver editor. Edit the values of one or more variables.
When you edit any variable value, the solid squares next to the previous
solution and leftNrt=diff disappear. Move the cursor to the variable for
which you now want to solve and press ƒ \.
TI-83 Plus
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77
Controlling the Solution for Solver or solve(
The TI-83 Plus solves equations through an iterative process. To control
that process, enter bounds that are relatively close to the solution and
enter an initial guess within those bounds. This will help to find a solution
more quickly. Also, it will define which solution you want for equations
with multiple solutions.
Using solve( on the Home Screen or from a Program
The function solve( is available only from CATALOG or from within a
program. It returns a solution (root) of expression for variable, given an
initial guess, and lower and upper bounds within which the solution is
sought. The default for lower is L1â99. The default for upper is 1â99. solve(
is valid only for real numbers.
solve(expression,variable,guess[,{lower,upper}])
expression is assumed equal to zero. The value of variable will not be
updated in memory. guess may be a value or a list of two values. Values
must be stored for every variable in expression, except variable, before
expression is evaluated. lower and upper must be entered in list format.
TI-83 Plus
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78
MATH NUM (Number) Operations
MATH NUM Menu
To display the MATH NUM menu, press ~.
MATH NUM
1:abs(
CPX PRB
Absolute value
Round
Integer part
2:round(
3:iPart(
4:fPart(
5:int(
Fractional part
Greatest integer
Minimum value
Maximum value
Least common multiple
Greatest common divisor
6:min(
7:max(
8:lcm(
9:gcd(
abs(
abs( (absolute value) returns the absolute value of real or complex
(modulus) numbers, expressions, lists, and matrices.
abs(value)
Note: abs( is also available on the MATH CPX menu.
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Math, Angle, and Test Operations
79
round(
round( returns a number, expression, list, or matrix rounded to #decimals
(9). If #decimals is omitted, value is rounded to the digits that are
displayed, up to 10 digits.
round(value[,#decimals])
iPart(, fPart(
iPart( (integer part) returns the integer part or parts of real or complex
numbers, expressions, lists, and matrices.
iPart(value)
fPart( (fractional part) returns the fractional part or parts of real or complex
numbers, expressions, lists, and matrices.
fPart(value)
TI-83 Plus
Math, Angle, and Test Operations
80
int(
int( (greatest integer) returns the largest integer real or complex
numbers, expressions, lists, and matrices.
int(value)
Note: For a given value, the result of int( is the same as the result of iPart( for
nonnegative numbers and negative integers, but one integer less than the
result of iPart( for negative noninteger numbers.
min(, max(
min( (minimum value) returns the smaller of valueA and valueB or the
smallest element in list. If listA and listB are compared, min( returns a list
of the smaller of each pair of elements. If list and value are compared,
min( compares each element in list with value.
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81
max( (maximum value) returns the larger of valueA and valueB or the
largest element in list. If listA and listB are compared, max( returns a list of
the larger of each pair of elements. If list and value are compared, max(
compares each element in list with value.
min(valueA,valueB)
min(list)
max(valueA,valueB)
max(list)
min(listA,listB)
min(list,value)
max(listA,listB)
max(list,value)
Note: min( and max( also are available on the LIST MATH menu.
lcm(, gcd(
lcm( returns the least common multiple of valueA and valueB, both of which
must be nonnegative integers. When listA and listB are specified, lcm(
returns a list of the lcm of each pair of elements. If list and value are
specified, lcm( finds the lcm of each element in list and value.
gcd( returns the greatest common divisor of valueA and valueB, both of
which must be nonnegative integers. When listA and listB are specified,
gcd( returns a list of the gcd of each pair of elements. If list and value are
specified, gcd( finds the gcd of each element in list and value.
TI-83 Plus
Math, Angle, and Test Operations
82
lcm(valueA,valueB)
lcm(listA,listB)
lcm(list,value)
gcd(valueA,valueB)
gcd(listA,listB)
gcd(list,value)
TI-83 Plus
Math, Angle, and Test Operations
83
Entering and Using Complex Numbers
Complex-Number Modes
The TI-83 Plus displays complex numbers in rectangular form and polar
form. To select a complex-number mode, press z, and then select
either of the two modes.
•
•
a+bi (rectangular-complex mode)
re^qi (polar-complex mode)
On the TI-83 Plus, complex numbers can be stored to variables. Also,
complex numbers are valid list elements.
In Real mode, complex-number results return an error, unless you
entered a complex number as input. For example, in Real mode ln(L1)
returns an error; in a+bi mode ln(L1) returns an answer.
TI-83 Plus
Math, Angle, and Test Operations
84
Real mode
a+bi mode
$
$
Entering Complex Numbers
Complex numbers are stored in rectangular form, but you can enter a
complex number in rectangular form or polar form, regardless of the
mode setting. The components of complex numbers can be real
numbers or expressions that evaluate to real numbers; expressions are
evaluated when the command is executed.
Note about Radian Versus Degree Mode
Radian mode is recommended for complex number calculations.
Internally, the TI-83 Plus converts all entered trigonometric values to
radians, but it does not convert values for exponential, logarithmic, or
hyperbolic functions.
In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are
not generally true because the values for cos and sin are converted to
radians, while those for e^() are not. For example, e^(i45) = cos(45)
+ i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex
identities are always true in radian mode.
TI-83 Plus
Math, Angle, and Test Operations
85
Interpreting Complex Results
Complex numbers in results, including list elements, are displayed in
either rectangular or polar form, as specified by the mode setting or by a
display conversion instruction. In the example below, polar-complex
(re^qi) and Radian modes are set.
Rectangular-Complex Mode
Rectangular-complex mode recognizes and displays a complex number in
the form a+bi, where a is the real component, b is the imaginary
component, and i is a constant equal to
.
-1
To enter a complex number in rectangular form, enter the value of a (real
component), press à or ¹, enter the value of b (imaginary component), and
press y V (constant).
TI-83 Plus
Math, Angle, and Test Operations
86
real component(+ or N)imaginary component i
Polar-Complex Mode
Polar-complex mode recognizes and displays a complex number in the
form re^qi, where r is the magnitude, e is the base of the natural log, q is the
angle, and i is a constant equal to
.
-1
To enter a complex number in polar form, enter the value of r (magnitude),
press y J (exponential function), enter the value of q (angle), press
y V (constant), and then press ¤.
magnitudee^(anglei)
TI-83 Plus
Math, Angle, and Test Operations
87
MATH CPX (Complex) Operations
MATH CPX Menu
To display the MATH CPX menu, press ~ ~.
MATH NUM CPX PRB
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
Returns the complex conjugate.
Returns the real part.
Returns the imaginary part.
Returns the polar angle.
Returns the magnitude (modulus).
Displays the result in rectangular form.
Displays the result in polar form.
6:4Rect
7:4Polar
conj(
conj( (conjugate) returns the complex conjugate of a complex number or
list of complex numbers.
conj(a+bi) returns aNbi in a+bi mode.
conj(re^(qi)) returns re^(Lqi) in re^qi mode.
TI-83 Plus
Math, Angle, and Test Operations
88
real(
real( (real part) returns the real part of a complex number or list of
complex numbers.
real(a+bi) returns a.
real(re^(qi)) returns räcos(q).
imag(
imag( (imaginary part) returns the imaginary (nonreal) part of a complex
number or list of complex numbers.
imag(a+bi) returns b.
imag(re^(qi)) returns räsin(q).
TI-83 Plus
Math, Angle, and Test Operations
89
angle(
angle( returns the polar angle of a complex number or list of complex
numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is
the real part. The calculation is adjusted by +p in the second quadrant or
Np in the third quadrant.
angle(a+bi) returns tanL1(b/a).
angle(re^(qi)) returns q, where Lp<q<p.
abs(
abs( (absolute value) returns the magnitude (modulus), (real2+imag2)
, of
a complex number or list of complex numbers.
abs(a+bi) returns (a2+b2)
.
abs(re^(qi)) returns r (magnitude).
TI-83 Plus
Math, Angle, and Test Operations
90
4Rect
4Rect (display as rectangular) displays a complex result in rectangular
form. It is valid only at the end of an expression. It is not valid if the result
is real.
complex result8Rect returns a+bi.
4Polar
4Polar (display as polar) displays a complex result in polar form. It is valid
only at the end of an expression. It is not valid if the result is real.
complex result8Polar returns re^(qi).
TI-83 Plus
Math, Angle, and Test Operations
91
MATH PRB (Probability) Operations
MATH PRB Menu
To display the MATH PRB menu, press |.
MATH NUM CPX PRB
1:rand
Random-number generator
Number of permutations
Number of combinations
Factorial
2:nPr
3:nCr
4:!
5:randInt(
6:randNorm(
7:randBin(
Random-integer generator
Random # from Normal distribution
Random # from Binomial distribution
rand
rand (random number) generates and returns one or more random
numbers > 0 and < 1. To generate a list of random-numbers, specify an
integer > 1 for numtrials (number of trials). The default for numtrials is 1.
rand[(numtrials)]
Tip: To generate random numbers beyond the range of 0 to 1, you can include
rand in an expression. For example, rand5 generates a random number > 0 and
< 5.
TI-83 Plus
Math, Angle, and Test Operations
92
With each rand execution, the TI-83 Plus generates the same random-
number sequence for a given seed value. The TI-83 Plus factory-set
seed value for rand is 0. To generate a different random-number
sequence, store any nonzero seed value to rand. To restore the factory-
set seed value, store 0 to rand or reset the defaults (Chapter 18).
Note: The seed value also affects randInt(, randNorm(, and randBin( instructions.
nPr, nCr
nPr (number of permutations) returns the number of permutations of items
taken number at a time. items and number must be nonnegative integers.
Both items and number can be lists.
items nPr number
nCr (number of combinations) returns the number of combinations of
items taken number at a time. items and number must be nonnegative
integers. Both items and number can be lists.
TI-83 Plus
Math, Angle, and Test Operations
93
items nCr number
! (Factorial)
! (factorial) returns the factorial of either an integer or a multiple of .5. For
a list, it returns factorials for each integer or multiple of .5. value must be
‚L.5 and 69.
value!
Note: The factorial is computed recursively using the relationship (n+1)! = nän!,
until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the
definition (L1à2)!=‡p is used to complete the calculation. Hence:
n!=nä(nN1)ä(nN2)ä ... ä2ä1, if n is an integer ‚0
n!= nä(nN1)ä(nN2)ä ... ä1à2ä‡p, if n+1à2 is an integer ‚0
n! is an error, if neither n nor n+1à2 is an integer ‚0.
(The variable n equals value in the syntax description above.)
TI-83 Plus
Math, Angle, and Test Operations
94
randInt(
randInt( (random integer) generates and displays a random integer within
a range specified by lower and upper integer bounds. To generate a list of
random numbers, specify an integer >1 for numtrials (number of trials); if
not specified, the default is 1.
randInt(lower,upper[,numtrials])
randNorm(
randNorm( (random Normal) generates and displays a random real
number from a specified Normal distribution. Each generated value could
be any real number, but most will be within the interval [mN3(s), m+3(s)].
To generate a list of random numbers, specify an integer > 1 for numtrials
(number of trials); if not specified, the default is 1.
randNorm(m,s[,numtrials])
TI-83 Plus
Math, Angle, and Test Operations
95
randBin(
randBin( (random Binomial) generates and displays a random integer
from a specified Binomial distribution. numtrials (number of trials) must be
‚ 1. prob (probability of success) must be ‚ 0 and 1. To generate a list
of random numbers, specify an integer > 1 for numsimulations (number of
simulations); if not specified, the default is 1.
randBin(numtrials,prob[,numsimulations])
Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin(
instructions.
TI-83 Plus
Math, Angle, and Test Operations
96
ANGLE Operations
ANGLE Menu
To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays
angle indicators and instructions. The Radian/Degree mode setting affects
the TI-83 Plus’s interpretation of ANGLE menu entries.
ANGLE
1:¡
Degree notation
2:'
DMS minute notation
Radian notation
r
3:
4:8DMS
Displays as degree/minute/second
Returns r, given X and Y
Returns q, given X and Y
Returns x, given R and q
Returns y, given R and q
5:R8Pr(
6:R8Pq(
7:P8Rx(
8:P8Ry(
Entry Notation
DMS (degrees/minutes/seconds) entry notation comprises the degree
symbol (¡), the minute symbol ('), and the second symbol ("). degrees
must be a real number; minutes and seconds must be real numbers ‚ 0.
degrees¡minutes'seconds"
TI-83 Plus
Math, Angle, and Test Operations
97
For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle
mode is not set to Degree, you must use ¡ so that the TI-83 Plus can
interpret the argument as degrees, minutes, and seconds.
Degree mode
Radian mode
¡ (Degree)
¡ (degree) designates an angle or list of angles as degrees, regardless of
the current angle mode setting. In Radian mode, you can use ¡ to convert
degrees to radians.
value¡
{value1,value2,value3,value4,...,value n}¡
¡ also designates degrees (D) in DMS format.
' (minutes) designates minutes (M) in DMS format.
" (seconds) designates seconds (S) in DMS format.
Note: " is not on the ANGLE menu. To enter ", press ƒ [ã].
TI-83 Plus
Math, Angle, and Test Operations
98
r (Radians)
r (radians) designates an angle or list of angles as radians, regardless of
the current angle mode setting. In Degree mode, you can use r to convert
radians to degrees.
r
value
Degree mode
8DMS
8DMS (degree/minute/second) displays answer in DMS format. The mode
setting must be Degree for answer to be interpreted as degrees, minutes,
and seconds. 8DMS is valid only at the end of a line.
answer8DMS
TI-83 Plus
Math, Angle, and Test Operations
99
R8Pr(, R8Pq(, P8Rx(, P8Ry(
R8Pr( converts rectangular coordinates to polar coordinates and returns
r. R8Pq( converts rectangular coordinates to polar coordinates and
returns q. x and y can be lists.
R8Pr(x,y), R8Pq(x,y)
Note: Radian mode is set.
P8Rx( converts polar coordinates to rectangular coordinates and returns
x. P8Ry( converts polar coordinates to rectangular coordinates and
returns y. r and q can be lists.
P8Rx(r,q), P8Ry(r,q)
Note: Radian mode is set.
TI-83 Plus
Math, Angle, and Test Operations
100
TEST (Relational) Operations
TEST Menu
To display the TEST menu, press y :.
This operator... Returns 1 (true) if...
TEST LOGIC
1:=
2:ƒ
3:>
4:‚
5:<
6:
Equal
Not equal to
Greater than
Greater than or equal to
Less than
Less than or equal to
=, ƒ, >, ‚, <,
Relational operators compare valueA and valueB and return 1 if the test is
true or 0 if the test is false. valueA and valueB can be real numbers,
expressions, or lists. For = and ƒ only, valueA and valueB also can be
matrices or complex numbers. If valueA and valueB are matrices, both
must have the same dimensions.
Relational operators are often used in programs to control program flow
and in graphing to control the graph of a function over specific values.
TI-83 Plus
Math, Angle, and Test Operations
101
valueA=valueB
valueA>valueB
valueA<valueB
valueAƒvalueB
valueA‚valueB
valueAvalueB
Using Tests
Relational operators are evaluated after mathematical functions
according to EOS rules (Chapter 1).
• The expression 2+2=2+3 returns 0. The TI-83 Plus performs the
addition first because of EOS rules, and then it compares 4 to 5.
• The expression 2+(2=2)+3 returns 6. The TI-83 Plus performs the
relational test first because it is in parentheses, and then it adds 2, 1,
and 3.
TI-83 Plus
Math, Angle, and Test Operations
102
TEST LOGIC (Boolean) Operations
TEST LOGIC Menu
To display the TEST LOGIC menu, press y ãTESTä ~.
This operator...
TEST LOGIC
1:and
Returns a 1 (true) if...
Both values are nonzero (true).
At least one value is nonzero (true).
Only one value is zero (false).
The value is zero (false).
2:or
3:xor
4:not(
Boolean Operators
Boolean operators are often used in programs to control program flow
and in graphing to control the graph of the function over specific values.
Values are interpreted as zero (false) or nonzero (true).
and, or, xor
and, or, and xor (exclusive or) return a value of 1 if an expression is true
or 0 if an expression is false, according to the table below. valueA and
valueB can be real numbers, expressions, or lists.
TI-83 Plus
Math, Angle, and Test Operations
103
valueA and valueB
valueA or valueB
valueA xor valueB
valueA
ƒ0
ƒ0
0
valueB
and
1
or
1
1
1
0
xor
0
ƒ0
0
returns
returns
returns
returns
0
1
ƒ0
0
0
1
0
0
0
not(
not( returns 1 if value (which can be an expression) is 0.
not(value)
Using Boolean Operations
Boolean logic is often used with relational tests. In the following program,
the instructions store 4 into C.
TI-83 Plus
Math, Angle, and Test Operations
104
Chapter 3:
Function Graphing
Getting Started: Graphing a Circle
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph a circle of radius 10, centered on the origin in the standard viewing
window. To graph this circle, you must enter separate formulas for the upper and
lower portions of the circle. Then use ZSquare (zoom square) to adjust the
display and make the functions appear as a circle.
1. In Func mode, press o to display the Y= editor.
Press y ã‡ä 100 ¹ „ ¡ ¤ Í to
enter the expression Y=‡(100NX2), which
defines the top half of the circle.
The expression Y=L‡(100NX2) defines the
bottom half of the circle. On the TI-83 Plus, you
can define one function in terms of another. To
define Y2=LY1, press Ì to enter the negation
sign. Press ~ to display the VARS Y.VARS
menu. Then press Í to select 1:Function.
The FUNCTION secondary menu is displayed.
Press 1 to select 1:Y1.
TI-83 Plus
Function Graphing
105
2. Press q 6 to select 6:ZStandard. This is a
quick way to reset the window variables to the
standard values. It also graphs the functions;
you do not need to press s.
Notice that the functions appear as an ellipse in
the standard viewing window.
3. To adjust the display so that each pixel
represents an equal width and height, press
q 5 to select 5:ZSquare. The functions are
replotted and now appear as a circle on the
display.
4. To see the ZSquare window variables, press
p and notice the new values for Xmin,
Xmax, Ymin, and Ymax.
TI-83 Plus
Function Graphing
106
Defining Graphs
TI-83 Plus—Graphing Mode Similarities
Chapter 3 specifically describes function graphing, but the steps shown
here are similar for each TI-83 Plus graphing mode. Chapters 4, 5, and 6
describe aspects that are unique to parametric graphing, polar graphing,
and sequence graphing.
Defining a Graph
To define a graph in any graphing mode, follow these steps. Some steps
are not always necessary.
1. Press z and set the appropriate graph mode.
2. Press o and enter, edit, or select one or more functions in the Y=
editor.
3. Deselect stat plots, if necessary.
4. Set the graph style for each function.
5. Press p and define the viewing window variables.
6. Press y . and select the graph format settings.
TI-83 Plus
Function Graphing
107
Displaying and Exploring a Graph
After you have defined a graph, press s to display it. Explore the
behavior of the function or functions using the TI-83 Plus tools described
in this chapter.
Saving a Graph for Later Use
You can store the elements that define the current graph to any of 10
graph database variables (GDB1 through GDB9, and GDB0; Chapter 8).
To recreate the current graph later, simply recall the graph database to
which you stored the original graph.
These types of information are stored in a GDB.
•
Y= functions
• Graph style settings
• Window settings
• Format settings
You can store a picture of the current graph display to any of 10 graph
picture variables (Pic1 through Pic9, and Pic0; Chapter 8). Then you can
superimpose one or more stored pictures onto the current graph.
TI-83 Plus
Function Graphing
108
Setting the Graph Modes
Checking and Changing the Graphing Mode
To display the mode screen, press z. The default settings are
highlighted below. To graph functions, you must select Func mode
before you enter values for the window variables and before you enter
the functions.
The TI-83 Plus has four graphing modes.
•
•
•
•
Func (function graphing)
Par (parametric graphing; Chapter 4)
Pol (polar graphing; Chapter 5)
Seq (sequence graphing; Chapter 6)
Other mode settings affect graphing results. Chapter 1 describes each
mode setting.
TI-83 Plus
Function Graphing
109
•
Float or 0123456789 (fixed) decimal mode affects displayed graph
coordinates.
•
•
•
Radian or Degree angle mode affects interpretation of some functions.
Connected or Dot plotting mode affects plotting of selected functions.
Sequential or Simul graphing-order mode affects function plotting
when more than one function is selected.
Setting Modes from a Program
To set the graphing mode and other modes from a program, begin on a
blank line in the program editor and follow these steps.
1. Press z to display the mode settings.
2. Press †, ~, |, and } to place the cursor on the mode that you
want to select.
3. Press Í to paste the mode name to the cursor location.
The mode is changed when the program is executed.
TI-83 Plus
Function Graphing
110
Defining Functions
Displaying Functions in the Y= Editor
To display the Y= editor, press o. You can store up to 10 functions to
the function variables Y1 through Y9, and Y0. You can graph one or more
defined functions at once. In this example, functions Y1 and Y2 are
defined and selected.
Defining or Editing a Function
To define or edit a function, follow these steps.
1. Press o to display the Y= editor.
2. Press † to move the cursor to the function you want to define or edit.
To erase a function, press ‘.
3. Enter or edit the expression to define the function.
TI-83 Plus
Function Graphing
111
• You may use functions and variables (including matrices and lists)
in the expression. When the expression evaluates to a nonreal
number, the value is not plotted; no error is returned.
• The independent variable in the function is X. Func mode defines
„ as X. To enter X, press „ or press ƒ [X].
• When you enter the first character, the = is highlighted, indicating
that the function is selected.
As you enter the expression, it is stored to the variable Yn as a user-
defined function in the Y= editor.
4. Press Í or † to move the cursor to the next function.
Defining a Function from the Home Screen or a Program
To define a function from the home screen or a program, begin on a
blank line and follow these steps.
1. Press ƒ [ã], enter the expression, and then press ƒ [ã]
again.
2. Press ¿.
3. Press ~ 1 to select 1:Function from the VARS Y.VARS menu.
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4. Select the function name, which pastes the name to the cursor
location on the home screen or program editor.
5. Press Í to complete the instruction.
"expression"!Yn
When the instruction is executed, the TI-83 Plus stores the expression to
the designated variable Yn, selects the function, and displays the
message Done.
Evaluating Y= Functions in Expressions
You can calculate the value of a Y= function Yn at a specified value of X. A
list of values returns a list.
Yn(value)
Yn({value1,value2,value3, . . .,value n})
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Selecting and Deselecting Functions
Selecting and Deselecting a Function
You can select and deselect (turn on and turn off) a function in the Y=
editor. A function is selected when the = sign is highlighted. The
TI-83 Plus graphs only the selected functions. You can select any or all
functions Y1 through Y9, and Y0.
To select or deselect a function in the Y= editor, follow these steps.
1. Press o to display the Y= editor.
2. Move the cursor to the function you want to select or deselect.
3. Press | to place the cursor on the function’s = sign.
4. Press Í to change the selection status.
When you enter or edit a function, it is selected automatically. When you
clear a function, it is deselected.
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Turning On or Turning Off a Stat Plot in the Y= Editor
To view and change the on/off status of a stat plot in the Y= editor, use
Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name
is highlighted on this line.
To change the on/off status of a stat plot from the Y= editor, press } and
~ to place the cursor on Plot1, Plot2, or Plot3, and then press Í.
Plot1 is turned on.
Plot2 and Plot3 are turned off.
Selecting and Deselecting Functions from the Home Screen or a
Program
To select or deselect a function from the home screen or a program,
begin on a blank line and follow these steps.
1. Press ~ to display the VARS Y.VARS menu.
2. Select 4:On/Off to display the ON/OFF secondary menu.
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3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off
one or more functions. The instruction you select is copied to the
cursor location.
4. Enter the number (1 through 9, or 0; not the variable Yn) of each
function you want to turn on or turn off.
• If you enter two or more numbers, separate them with commas.
• To turn on or turn off all functions, do not enter a number after
FnOn or FnOff.
FnOn[function#,function#, . . .,function n]
FnOff[function#,function#, . . .,function n]
5. Press Í. When the instruction is executed, the status of each
function in the current mode is set and Done is displayed.
For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the
Y= editor, and then turns on Y1 and Y3.
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Setting Graph Styles for Functions
Graph Style Icons in the Y= Editor
This table describes the graph styles available for function graphing. Use
the styles to visually differentiate functions to be graphed together. For
example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a
thick line.
Icon
Style
Description
ç
Line
A solid line connects plotted points; this is the default in
Connected mode
è
é
ê
ë
Thick
Above
Below
Path
A thick solid line connects plotted points
Shading covers the area above the graph
Shading covers the area below the graph
A circular cursor traces the leading edge of the graph and
draws a path
ì
Animate
Dot
A circular cursor traces the leading edge of the graph
without drawing a path
í
A small dot represents each plotted point; this is the
default in Dot mode
Note: Some graph styles are not available in all graphing modes. Chapters 4,
5, and 6 list the styles for Par, Pol, and Seq modes.
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Setting the Graph Style
To set the graph style for a function, follow these steps.
1. Press o to display the Y= editor.
2. Press † and } to move the cursor to the function.
3. Press | | to move the cursor left, past the = sign, to the graph style
icon in the first column. The insert cursor is displayed. (Steps 2 and 3
are interchangeable.)
4. Press Í repeatedly to rotate through the graph styles. The seven
styles rotate in the same order in which they are listed in the table
above.
5. Press ~, }, or † when you have selected a style.
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Shading Above and Below
When you select é or ê for two or more functions, the TI-83 Plus rotates
through four shading patterns.
• Vertical lines shade the first function with a é or ê graph style.
• Horizontal lines shade the second.
• Negatively sloping diagonal lines shade the third.
• Positively sloping diagonal lines shade the fourth.
• The rotation returns to vertical lines for the fifth é or ê function,
repeating the order described above.
When shaded areas intersect, the patterns overlap.
Note: When é or ê is selected for a Y= function that graphs a family of curves,
such as Y1={1,2,3}X, the four shading patterns rotate for each member of the
family of curves.
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Setting a Graph Style from a Program
To set the graph style from a program, select H:GraphStyle( from the
PRGM CTL menu. To display this menu, press while in the program
editor. function# is the number of the Y= function name in the current
graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to
the graph style, as shown below.
1 = ç (line)
2 = è (thick)
3 = é (above)
4 = ê (below)
5 = ë (path)
6 = ì (animate)
7 = í (dot)
GraphStyle(function#,graphstyle#)
For example, when this program is executed in Func mode,
GraphStyle(1,3) sets Y1 to é (above).
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Setting the Viewing Window Variables
The TI-83 Plus Viewing Window
The viewing window is the portion of the coordinate plane defined by
Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) defines the distance between
tick marks on the x-axis. Yscl (Y scale) defines the distance between tick
marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0.
Ymax
Xscl
Xmin
Xmax
Yscl
Ymin
Displaying the Window Variables
To display the current window variable values, press p. The
window editor above and to the right shows the default values in Func
graphing mode and Radian angle mode. The window variables differ from
one graphing mode to another.
Xres sets pixel resolution (1 through 8) for function graphs only. The
default is 1.
• At Xres=1, functions are evaluated and graphed at each pixel on the
x-axis.
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• At Xres=8, functions are evaluated and graphed at every eighth pixel
along the x-axis.
Tip: Small Xres values improve graph resolution but may cause the TI-83 Plus
to draw graphs more slowly.
Changing a Window Variable Value
To change a window variable value from the window editor, follow these
steps.
1. Press † or } to move the cursor to the window variable you want to
change.
2. Edit the value, which can be an expression.
• Enter a new value, which clears the original value.
• Move the cursor to a specific digit, and then edit it.
3. Press Í, †, or }. If you entered an expression, the TI-83 Plus
evaluates it. The new value is stored.
Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph.
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Storing to a Window Variable from the Home Screen or a Program
To store a value, which can be an expression, to a window variable,
begin on a blank line and follow these steps.
1. Enter the value you want to store.
2. Press ¿.
3. Press to display the VARS menu.
4. Select 1:Window to display the Func window variables (X/Y secondary
menu).
• Press ~ to display the Par and Pol window variables (T/q
secondary menu).
• Press ~ ~ to display the Seq window variables (U/V/W secondary
menu).
5. Select the window variable to which you want to store a value. The
name of the variable is pasted to the current cursor location.
6. Press Í to complete the instruction.
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When the instruction is executed, the TI-83 Plus stores the value to the
window variable and displays the value.
@X and @Y
The variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y
secondary menu) define the distance from the center of one pixel to the
center of any adjacent pixel on a graph (graphing accuracy). @X and @Y
are calculated from Xmin, Xmax, Ymin, and Ymax when you display a
graph.
(Xmax N Xmin)
(Ymax N Ymin)
@X =
@Y =
94
62
You can store values to @X and @Y. If you do, Xmax and Ymax are
calculated from @X, Xmin, @Y, and Ymin.
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Setting the Graph Format
Displaying the Format Settings
To display the format settings, press y .. The default settings
are highlighted below.
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Sets cursor coordinates.
Sets coordinates display on or off.
Sets grid off or on.
Sets axes on or off.
Sets axes label off or on.
Sets expression display on or off.
Format settings define a graph’s appearance on the display. Format
settings apply to all graphing modes. Seq graphing mode has an
additional mode setting (Chapter 6).
Changing a Format Setting
To change a format setting, follow these steps.
1. Press †, ~, }, and | as necessary to move the cursor to the
setting you want to select.
2. Press Í to select the highlighted setting.
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RectGC, PolarGC
RectGC (rectangular graphing coordinates) displays the cursor location
as rectangular coordinates X and Y.
PolarGC (polar graphing coordinates) displays the cursor location as
polar coordinates R and q.
The RectGC/PolarGC setting determines which variables are updated
when you plot the graph, move the free-moving cursor, or trace.
•
•
RectGC updates X and Y; if CoordOn format is selected, X and Y are
displayed.
PolarGC updates X, Y, R, and q; if CoordOn format is selected, R and q
are displayed.
CoordOn, CoordOff
CoordOn (coordinates on) displays the cursor coordinates at the bottom
of the graph. If ExprOff format is selected, the function number is
displayed in the top-right corner.
CoordOff (coordinates off) does not display the function number or
coordinates.
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GridOff, GridOn
Grid points cover the viewing window in rows that correspond to the tick
marks on each axis.
GridOff does not display grid points.
GridOn displays grid points.
AxesOn, AxesOff
AxesOn displays the axes.
AxesOff does not display the axes.
This overrides the LabelOff/LabelOn format setting.
LabelOff, LabelOn
LabelOff and LabelOn determine whether to display labels for the axes (X
and Y), if AxesOn format is also selected.
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ExprOn, ExprOff
ExprOn and ExprOff determine whether to display the Y= expression
when the trace cursor is active. This format setting also applies to stat
plots.
When ExprOn is selected, the expression is displayed in the top-left
corner of the graph screen.
When ExprOff and CoordOn both are selected, the number in the top-right
corner specifies which function is being traced.
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Displaying Graphs
Displaying a New Graph
To display the graph of the selected function or functions, press s.
TRACE, ZOOM instructions, and CALC operations display the graph
automatically. As the TI-83 Plus plots the graph, the busy indicator is on.
As the graph is plotted, X and Y are updated.
Pausing or Stopping a Graph
While plotting a graph, you can pause or stop graphing.
• Press Í to pause; then press Í to resume.
• Press É to stop; then press s to redraw.
Smart Graph
Smart Graph is a TI-83 Plus feature that redisplays the last graph
immediately when you press s, but only if all graphing factors that
would cause replotting have remained the same since the graph was last
displayed.
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If you performed any of these actions since the graph was last displayed,
the TI-83 Plus will replot the graph based on new values when you press
s.
• Changed a mode setting that affects graphs
• Changed a function in the current picture
• Selected or deselected a function or stat plot
• Changed the value of a variable in a selected function
• Changed a window variable or graph format setting
• Cleared drawings by selecting ClrDraw
• Changed a stat plot definition
Overlaying Functions on a Graph
On the TI-83 Plus, you can graph one or more new functions without
replotting existing functions. For example, store sin(X) to Y1 in the
Y= editor and press s. Then store cos(X) to Y2 and press s
again. The function Y2 is graphed on top of Y1, the original function.
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Graphing a Family of Curves
If you enter a list (Chapter 11) as an element in an expression, the
TI-83 Plus plots the function for each value in the list, thereby graphing a
family of curves. In Simul graphing-order mode, it graphs all functions
sequentially for the first element in each list, and then for the second,
and so on.
{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X).
{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X).
Note: When using more than one list, the lists must have the same dimensions.
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Exploring Graphs with the Free-Moving
Cursor
Free-Moving Cursor
When a graph is displayed, press |, ~, }, or † to move the cursor
around the graph. When you first display the graph, no cursor is visible.
When you press |, ~, }, or †, the cursor moves from the center of the
viewing window.
As you move the cursor around the graph, the coordinate values of the
cursor location are displayed at the bottom of the screen if CoordOn
format is selected. The Float/Fix decimal mode setting determines the
number of decimal digits displayed for the coordinate values.
To display the graph with no cursor and no coordinate values, press
‘ or Í. When you press |, ~, }, or †, the cursor moves from
the same position.
Graphing Accuracy
The free-moving cursor moves from pixel to pixel on the screen. When
you move the cursor to a pixel that appears to be on the function, the
cursor may be near, but not actually on, the function. The coordinate
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value displayed at the bottom of the screen actually may not be a point
on the function. To move the cursor along a function, use r.
The coordinate values displayed as you move the cursor approximate
actual math coordinates, *accurate to within the width and height of the
pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoom
In) graphing accuracy increases, and the coordinate values more closely
approximate the math coordinates.
Free- moving cursor “on” the
curve
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Exploring Graphs with TRACE
Beginning a Trace
Use TRACE to move the cursor from one plotted point to the next along a
function. To begin a trace, press r. If the graph is not displayed
already, press r to display it. The trace cursor is on the first
selected function in the Y= editor, at the middle X value on the screen.
The cursor coordinates are displayed at the bottom of the screen if
CoordOn format is selected. The Y= expression is displayed in the top-left
corner of the screen, if ExprOn format is selected.
Moving the Trace Cursor
To move the TRACE cursor
do this:
To the previous or next plotted point,
press | or ~.
Five plotted points on a function (Xres
affects this),
press y | or y ~.
enter a value, and then press Í.
press } or †.
To any valid X value on a function,
From one function to another,
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When the trace cursor moves along a function, the Y value is calculated
from the X value; that is, Y=Yn(X). If the function is undefined at an X
value, the Y value is blank.
Trace cursor on the
curve
If you move the trace cursor beyond the top or bottom of the screen, the
coordinate values at the bottom of the screen continue to change
appropriately.
Moving the Trace Cursor from Function to Function
To move the trace cursor from function to function, press † and }. The
cursor follows the order of the selected functions in the Y= editor. The
trace cursor moves to each function at the same X value. If ExprOn
format is selected, the expression is updated.
Moving the Trace Cursor to Any Valid X Value
To move the trace cursor to any valid X value on the current function,
enter the value. When you enter the first digit, an X= prompt and the
number you entered are displayed in the bottom-left corner of the
screen. You can enter an expression at the X= prompt. The value must
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be valid for the current viewing window. When you have completed the
entry, press Í to move the cursor.
Note: This feature does not apply to stat plots.
Panning to the Left or Right
If you trace a function beyond the left or right side of the screen, the
viewing window automatically pans to the left or right. Xmin and Xmax are
updated to correspond to the new viewing window.
Quick Zoom
While tracing, you can press Í to adjust the viewing window so that
the cursor location becomes the center of the new viewing window, even
if the cursor is above or below the display. This allows panning up and
down. After Quick Zoom, the cursor remains in TRACE.
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Leaving and Returning to TRACE
When you leave and return to TRACE, the trace cursor is displayed in the
same location it was in when you left TRACE, unless Smart Graph has
replotted the graph.
Using TRACE in a Program
On a blank line in the program editor, press r. The instruction Trace
is pasted to the cursor location. When the instruction is encountered
during program execution, the graph is displayed with the trace cursor on
the first selected function. As you trace, the cursor coordinate values are
updated. When you finish tracing the functions, press Í to resume
program execution.
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Exploring Graphs with the ZOOM
Instructions
ZOOM Menu
To display the ZOOM menu, press q. You can adjust the viewing
window of the graph quickly in several ways. All ZOOM instructions are
accessible from programs.
ZOOM MEMORY
1:ZBox
Draws a box to define the viewing window.
Magnifies the graph around the cursor.
Views more of a graph around the cursor.
Sets @X and @Y to 0.1.
Sets equal-size pixels on the X and Y axes.
Sets the standard window variables.
Sets the built-in trig window variables.
Sets integer values on the X and Y axes.
Sets the values for current stat lists.
Fits YMin and YMax between XMin and XMax.
2:Zoom In
3:Zoom Out
4:ZDecimal
5:ZSquare
6:ZStandard
7:ZTrig
8:ZInteger
9:ZoomStat
0:ZoomFit
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Zoom Cursor
When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the
graph becomes the zoom cursor (+), a smaller version of the free-moving
cursor (+).
ZBox
To define a new viewing window using ZBox, follow these steps.
1. Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at
the center of the screen.
2. Move the zoom cursor to any spot you want to define as a corner of
the box, and then press Í. When you move the cursor away from
the first defined corner, a small, square dot indicates the spot.
3. Press |, }, ~, or †. As you move the cursor, the sides of the box
lengthen or shorten proportionately on the screen.
Note: To cancel ZBox before you press Í, press ‘.
4. When you have defined the box, press Í to replot the graph.
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To use ZBox to define another box within the new graph, repeat steps 2
through 4. To cancel ZBox, press ‘.
Zoom In, Zoom Out
Zoom In magnifies the part of the graph that surrounds the cursor
location. Zoom Out displays a greater portion of the graph, centered on
the cursor location. The XFact and YFact settings determine the extent of
the zoom.
To zoom in on a graph, follow these steps.
1. Check XFact and YFact; change as needed.
2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed.
3. Move the zoom cursor to the point that is to be the center of the new
viewing window.
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4. Press Í. The TI-83 Plus adjusts the viewing window by XFact and
YFact; updates the window variables; and replots the selected
functions, centered on the cursor location.
5. Zoom in on the graph again in either of two ways.
• To zoom in at the same point, press Í.
• To zoom in at a new point, move the cursor to the point that you
want as the center of the new viewing window, and then press
Í.
To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5.
To cancel Zoom In or Zoom Out, press ‘.
ZDecimal
ZDecimal replots the functions immediately. It updates the window
variables to preset values, as shown below. These values set @X and @Y
equal to 0.1 and set the X and Y value of each pixel to one decimal place.
Xmin=L4.7
Xmax=4.7
Xscl=1
Ymin=L3.1
Ymax=3.1
Yscl=1
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ZSquare
ZSquare replots the functions immediately. It redefines the viewing
window based on the current values of the window variables. It adjusts in
only one direction so that @X=@Y, which makes the graph of a circle look
like a circle. Xscl and Yscl remain unchanged. The midpoint of the
current graph (not the intersection of the axes) becomes the midpoint of
the new graph.
ZStandard
ZStandard replots the functions immediately. It updates the window
variables to the standard values shown below.
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Xres=1
ZTrig
ZTrig replots the functions immediately. It updates the window variables
to preset values that are appropriate for plotting trig functions. Those
preset values in Radian mode are shown below.
Xmin=L(47à24)p
Xmax=(47à24)p
Xscl=p/2
Ymin=L4
Ymax=4
Yscl=1
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ZInteger
ZInteger redefines the viewing window to the dimensions shown below.
To use ZInteger, move the cursor to the point that you want to be the
center of the new window, and then press Í; ZInteger replots the
functions.
@X=1
@Y=1
Xscl=10
Yscl=10
ZoomStat
ZoomStat redefines the viewing window so that all statistical data points
are displayed. For regular and modified box plots, only Xmin and Xmax
are adjusted.
ZoomFit
ZoomFit replots the functions immediately. ZoomFit recalculates YMin and
YMax to include the minimum and maximum Y values of the selected
functions between the current XMin and XMax. XMin and XMax are not
changed.
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Using ZOOM MEMORY
ZOOM MEMORY Menu
To display the ZOOM MEMORY menu, press q ~.
ZOOM MEMORY
1:ZPrevious
2:ZoomSto
Uses the previous viewing window.
Stores the user-defined window.
Recalls the user-defined window.
Changes Zoom In and Zoom Out factors.
3:ZoomRcl
4:SetFactors...
ZPrevious
ZPrevious replots the graph using the window variables of the graph that
was displayed before you executed the last ZOOM instruction.
ZoomSto
ZoomSto immediately stores the current viewing window. The graph is
displayed, and the values of the current window variables are stored in
the user-defined ZOOM variables ZXmin, ZXmax, ZXscl, ZYmin, ZYmax,
ZYscl, and ZXres.
These variables apply to all graphing modes. For example, changing the
value of ZXmin in Func mode also changes it in Par mode.
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ZoomRcl
ZoomRcl graphs the selected functions in a user-defined viewing window.
The user-defined viewing window is determined by the values stored
with the ZoomSto instruction. The window variables are updated with the
user-defined values, and the graph is plotted.
ZOOM FACTORS
The zoom factors, XFact and YFact, are positive numbers (not
necessarily integers) greater than or equal to 1. They define the
magnification or reduction factor used to Zoom In or Zoom Out around a
point.
Checking XFact and YFact
To display the ZOOM FACTORS screen, where you can review the current
values for XFact and YFact, select 4:SetFactors from the ZOOM MEMORY
menu. The values shown are the defaults.
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Changing XFact and YFact
You can change XFact and YFact in either of two ways.
• Enter a new value. The original value is cleared automatically when
you enter the first digit.
• Place the cursor on the digit you want to change, and then enter a
value or press { to delete it.
Using ZOOM MEMORY Menu Items from the Home Screen or a
Program
From the home screen or a program, you can store directly to any of the
user-defined ZOOM variables.
From a program, you can select the ZoomSto and ZoomRcl instructions
from the ZOOM MEMORY menu.
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Using the CALC (Calculate) Operations
CALCULATE Menu
To display the CALCULATE menu, press y ãCALCä. Use the items on this
menu to analyze the current graph functions.
CALCULATE
1:value
Calculates a function Y value for a given X.
Finds a zero (x-intercept) of a function.
Finds a minimum of a function.
2:zero
3:minimum
4:maximum
5:intersect
6:dy/dx
Finds a maximum of a function.
Finds an intersection of two functions.
Finds a numeric derivative of a function.
Finds a numeric integral of a function.
7:‰f(x)dx
value
value evaluates one or more currently selected functions for a specified
value of X.
Note: When a value is displayed for X, press ‘ to clear the value. When no
value is displayed, press ‘ to cancel the value operation.
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To evaluate a selected function at X, follow these steps.
1. Select 1:value from the CALCULATE menu. The graph is displayed with
X= in the bottom-left corner.
2. Enter a real value, which can be an expression, for X between Xmin
and Xmax.
3. Press Í.
The cursor is on the first selected function in the Y= editor at the X value
you entered, and the coordinates are displayed, even if CoordOff format
is selected.
To move the cursor from function to function at the entered X value,
press } or †. To restore the free-moving cursor, press | or ~.
zero
zero finds a zero (x-intercept or root) of a function using solve(. Functions
can have more than one x-intercept value; zero finds the zero closest to
your guess.
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The time zero spends to find the correct zero value depends on the
accuracy of the values you specify for the left and right bounds and the
accuracy of your guess.
To find a zero of a function, follow these steps.
1. Select 2:zero from the CALCULATE menu. The current graph is
displayed with Left Bound? in the bottom-left corner.
2. Press } or † to move the cursor onto the function for which you
want to find a zero.
3. Press | or ~ (or enter a value) to select the x-value for the left
bound of the interval, and then press Í. A 4 indicator on the
graph screen shows the left bound. Right Bound? is displayed in the
bottom-left corner. Press | or ~ (or enter a value) to select the
x-value for the right bound, and then press Í. A 3 indicator on the
graph screen shows the right bound. Guess? is then displayed in the
bottom-left corner.
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4. Press | or ~ (or enter a value) to select a point near the zero of the
function, between the bounds, and then press Í.
The cursor is on the solution and the coordinates are displayed, even if
CoordOff format is selected. To move to the same x-value for other
selected functions, press } or †. To restore the free-moving cursor,
press | or ~.
minimum, maximum
minimum and maximum find a minimum or maximum of a function within
a specified interval to a tolerance of 1âL5.
To find a minimum or maximum, follow these steps.
1. Select 3:minimum or 4:maximum from the CALCULATE menu. The
current graph is displayed.
2. Select the function and set left bound, right bound, and guess as
described for zero.
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The cursor is on the solution, and the coordinates are displayed, even if
you have selected CoordOff format; Minimum or Maximum is displayed in
the bottom-left corner.
To move to the same x-value for other selected functions, press } or †.
To restore the free-moving cursor, press | or ~.
intersect
intersect finds the coordinates of a point at which two or more functions
intersect using solve(. The intersection must appear on the display to use
intersect.
To find an intersection, follow these steps.
1. Select 5:intersect from the CALCULATE menu. The current graph is
displayed with First curve? in the bottom-left corner.
2. Press † or }, if necessary, to move the cursor to the first function,
and then press Í. Second curve? is displayed in the bottom-left
corner.
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3. Press † or }, if necessary, to move the cursor to the second
function, and then press Í.
4. Press ~ or | to move the cursor to the point that is your guess as to
location of the intersection, and then press Í.
The cursor is on the solution and the coordinates are displayed, even if
CoordOff format is selected. Intersection is displayed in the bottom-left
corner. To restore the free-moving cursor, press |, }, ~, or †.
dy/dx
dy/dx (numerical derivative) finds the numerical derivative (slope) of a
function at a point, with H=1âL3.
To find a function’s slope at a point, follow these steps.
1. Select 6:dy/dx from the CALCULATE menu. The current graph is
displayed.
2. Press } or † to select the function for which you want to find the
numerical derivative.
3. Press | or ~ (or enter a value) to select the X value at which to
calculate the derivative, and then press Í.
The cursor is on the solution and the numerical derivative is displayed.
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To move to the same x-value for other selected functions, press } or †.
To restore the free-moving cursor, press | or ~.
‰f(x)dx
‰f(x)dx (numerical integral) finds the numerical integral of a function in a
specified interval. It uses the fnInt( function, with a tolerance of H=1âL3.
To find the numerical derivative of a function, follow these steps.
1. Select 7:‰f(x)dx from the CALCULATE menu. The current graph is
displayed with Lower Limit? in the bottom-left corner.
2. Press } or † to move the cursor to the function for which you want
to calculate the integral.
3. Set lower and upper limits as you would set left and right bounds for
zero. The integral value is displayed, and the integrated area is
shaded.
Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action
that invokes Smart Graph to clear the shaded area.
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Chapter 4:
Parametric Graphing
Getting Started: Path of a Ball
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph the parametric equation that describes the path of a ball hit at an initial
speed of 30 meters per second, at an initial angle of 25 degrees with the
horizontal from ground level. How far does the ball travel? When does it hit the
ground? How high does it go? Ignore all forces except gravity.
For initial velocity v0 and angle q, the position of the ball as a function of time has
horizontal and vertical components.
1
2
Horizontal: X1(t)=tv cos(q)
Vertical: Y1(t)=tv sin(q)N gt
0
0
2
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector:
Horizontal vector:
Gravity constant:
X2(t)=0
X3(t)=X1(t)
g=9.8 m/sec
Y2(t)=Y1(t)
Y3(t)=0
2
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1. Press z. Press † † † ~ Í to select
Par mode. Press † † ~ Í to select Simul
for simultaneous graphing of all three
parametric equations in this example.
2. Press o. Press 30 „ ™ 25 y ; 1
(to select ¡) ¤ Í to define X1T in terms of T.
3. Press 30 „ ˜ 25 y ; 1 ¤ ¹ 9.8
¥ 2 „ ¡ Í to define Y1T.
The vertical component vector is defined by X2T
and Y2T.
4. Press 0 Í to define X2T.
5. Press ~ to display the VARS Y.VARS menu.
Press 2 to display the PARAMETRIC secondary
menu. Press 2 Í to define Y2T.
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The horizontal component vector is defined by
X3T and Y3T.
6. Press ~ 2, and then press 1 Í to
define X3T. Press 0 Í to define Y3T.
7. Press | | } Í to change the graph style
to è for X3T and Y3T. Press } Í Í to
change the graph style to ë for X2T and Y2T.
Press } Í Í to change the graph style
to ë for X1T and Y1T. (These keystrokes assume
that all graph styles were set to ç originally.)
8. Press p. Enter these values for the
window variables.
Tmin=0
Tmax=5
Tstep=.1
Xmin=L10
Xmax=100
Xscl=50
Ymin=L5
Ymax=15
Yscl=10
9. Press y . † † † ~ Í to set
AxesOff, which turns off the axes.
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10.Press s. The plotting action
simultaneously shows the ball in flight and the
vertical and horizontal component vectors of the
motion.
Tip: To simulate the ball flying through the air, set
graph style to ì (animate) for X1T and Y1T.
11.Press r to obtain numerical results and
answer the questions at the beginning of this
section.
Tracing begins at Tmin on the first parametric
equation (X1T and Y1T). As you press ~ to trace
the curve, the cursor follows the path of the ball
over time. The values for X (distance), Y
(height), and T (time) are displayed at the
bottom of the screen.
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Defining and Displaying Parametric Graphs
TI-83 Plus Graphing Mode Similarities
The steps for defining a parametric graph are similar to the steps for
defining a function graph. Chapter 4 assumes that you are familiar with
Chapter 3: Function Graphing. Chapter 4 details aspects of parametric
graphing that differ from function graphing.
Setting Parametric Graphing Mode
To display the mode screen, press z. To graph parametric equations,
you must select Par graphing mode before you enter window variables
and before you enter the components of parametric equations.
Displaying the Parametric Y= Editor
After selecting Par graphing mode, press o to display the parametric Y=
editor.
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In this editor, you can display and enter both the X and Y components of
up to six equations, X1T and Y1T through X6T and Y6T. Each is defined in
terms of the independent variable T. A common application of parametric
graphs is graphing equations over time.
Selecting a Graph Style
The icons to the left of X1T through X6T represent the graph style of each
parametric equation (Chapter 3). The default in Par mode is ç (line),
which connects plotted points. Line, è (thick), ë (path), ì (animate), and í
(dot) styles are available for parametric graphing.
Defining and Editing Parametric Equations
To define or edit a parametric equation, follow the steps in Chapter 3 for
defining a function or editing a function. The independent variable in a
parametric equation is T. In Par graphing mode, you can enter the
parametric variable T in either of two ways.
• Press „.
• Press ƒ ãTä.
Two components, X and Y, define a single parametric equation. You
must define both of them.
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Selecting and Deselecting Parametric Equations
The TI-83 Plus graphs only the selected parametric equations. In the Y=
editor, a parametric equation is selected when the = signs of both the
X and Y components are highlighted. You may select any or all of the
equations X1T and Y1T through X6T and Y6T.
To change the selection status, move the cursor onto the = sign of either
the X or Y component and press Í. The status of both the X and Y
components is changed.
Setting Window Variables
To display the window variable values, press p. These variables
define the viewing window. The values below are defaults for Par
graphing in Radian angle mode.
Tmin=0
Smallest T value to evaluate
Tmax=6.2831853...
Tstep=.1308996...
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Largest T value to evaluate (2p)
T value increment (pà24)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Note: To ensure that sufficient points are plotted, you may want to change the T
window variables.
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Setting the Graph Format
To display the current graph format settings, press y .. Chapter
3 describes the format settings in detail. The other graphing modes
share these format settings; Seq graphing mode has an additional axes
format setting.
Displaying a Graph
When you press s, the TI-83 Plus plots the selected parametric
equations. It evaluates the X and Y components for each value of T (from
Tmin to Tmax in intervals of Tstep), and then plots each point defined by
X and Y. The window variables define the viewing window.
As the graph is plotted, X, Y, and T are updated.
Smart Graph applies to parametric graphs (Chapter 3).
Window Variables and Y.VARS Menus
You can perform these actions from the home screen or a program.
• Access functions by using the name of the X or Y component of the
equation as a variable.
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• Store parametric equations.
• Select or deselect parametric equations.
• Store values directly to window variables.
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Exploring Parametric Graphs
Free-Moving Cursor
The free-moving cursor in Par graphing works the same as in Func
graphing.
In RectGC format, moving the cursor updates the values of X and Y; if
CoordOn format is selected, X and Y are displayed.
In PolarGC format, X, Y, R, and q are updated; if CoordOn format is
selected, R and q are displayed.
TRACE
To activate TRACE, press r. When TRACE is active, you can move the
trace cursor along the graph of the equation one Tstep at a time. When
you begin a trace, the trace cursor is on the first selected function at
Tmin. If ExprOn is selected, then the function is displayed.
In RectGC format, TRACE updates and displays the values of X, Y, and T if
CoordOn format is on.
In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is
selected, R, q, and T are displayed. The X and Y (or R and q) values are
calculated from T.
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To move five plotted points at a time on a function, press y | or
y ~. If you move the cursor beyond the top or bottom of the screen,
the coordinate values at the bottom of the screen continue to change
appropriately.
Quick Zoom is available in Par graphing; panning is not (Chapter 3).
Moving the Trace Cursor to Any Valid T Value
To move the trace cursor to any valid T value on the current function,
enter the number. When you enter the first digit, a T= prompt and the
number you entered are displayed in the bottom-left corner of the
screen. You can enter an expression at the T= prompt. The value must
be valid for the current viewing window. When you have completed the
entry, press Í to move the cursor.
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ZOOM
ZOOM operations in Par graphing work the same as in Func graphing.
Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window
variables are affected.
The T window variables (Tmin, Tmax, and Tstep) are only affected when
you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items
1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for Par
graphing.
CALC
CALC operations in Par graphing work the same as in Func graphing. The
CALCULATE menu items available in Par graphing are 1:value, 2:dy/dx,
3:dy/dt, and 4:dx/dt.
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Chapter 5:
Polar Graphing
Getting Started: Polar Rose
Getting Started is a fast-paced introduction. Read the chapter for details.
The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5,
and then explore the appearance of the rose for other values of A and B.
1. Press z to display the mode screen. Press
† † † ~ ~ Í to select Pol graphing
mode. Select the defaults (the options on the
left) for the other mode settings.
2. Press o to display the polar Y= editor. Press 8
˜ 2.5 „ ¤ Í to define r1.
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3. Press q 6 to select 6:ZStandard and graph
the equation in the standard viewing window.
The graph shows only five petals of the rose,
and the rose does not appear to be
symmetrical. This is because the standard
window sets qmax=2p and defines the window,
rather than the pixels, as square.
4. Press p to display the window variables.
Press † 4 y B to increase the value of qmax
to 4p.
5. Press q 5 to select 5:ZSquare and plot the
graph.
6. Repeat steps 2 through 5 with new values for
the variables A and B in the polar equation
r1=Asin(Bq). Observe how the new values affect
the graph.
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167
Defining and Displaying Polar Graphs
TI-83 Plus Graphing Mode Similarities
The steps for defining a polar graph are similar to the steps for defining a
function graph. Chapter 5 assumes that you are familiar with Chapter 3:
Function Graphing. Chapter 5 details aspects of polar graphing that differ
from function graphing.
Setting Polar Graphing Mode
To display the mode screen, press z. To graph polar equations, you
must select Pol graphing mode before you enter values for the window
variables and before you enter polar equations.
Displaying the Polar Y= Editor
After selecting Pol graphing mode, press o to display the polar
Y= editor.
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In this editor, you can enter and display up to six polar equations, r1
through r6. Each is defined in terms of the independent variable q.
Selecting Graph Styles
The icons to the left of r1 through r6 represent the graph style of each
polar equation (Chapter 3). The default in Pol graphing mode is ç (line),
which connects plotted points. Line, è (thick), ë (path), ì (animate), and í
(dot) styles are available for polar graphing.
Defining and Editing Polar Equations
To define or edit a polar equation, follow the steps in Chapter 3 for
defining a function or editing a function. The independent variable in a
polar equation is q. In Pol graphing mode, you can enter the polar
variable q in either of two ways.
• Press „.
• Press ƒ ãqä.
Selecting and Deselecting Polar Equations
The TI-83 Plus graphs only the selected polar equations. In the Y= editor,
a polar equation is selected when the = sign is highlighted. You may
select any or all of the equations.
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To change the selection status, move the cursor onto the = sign, and
then press Í.
Setting Window Variables
To display the window variable values, press p. These variables
define the viewing window. The values below are defaults for Pol
graphing in Radian angle mode.
qmin=0
Smallest q value to evaluate
qmax=6.2831853...
qstep=.1308996...
Xmin=L10
Largest q value to evaluate (2p)
Increment between q values (pà24)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Note: To ensure that sufficient points are plotted, you may want to change the q
window variables.
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Setting the Graph Format
To display the current graph format settings, press y .. Chapter
3 describes the format settings in detail. The other graphing modes
share these format settings.
Displaying a Graph
When you press s, the TI-83 Plus plots the selected polar
equations. It evaluates R for each value of q (from qmin to qmax in
intervals of qstep) and then plots each point. The window variables define
the viewing window.
As the graph is plotted, X, Y, R, and q are updated.
Smart Graph applies to polar graphs (Chapter 3).
Window Variables and Y.VARS Menus
You can perform these actions from the home screen or a program.
• Access functions by using the name of the equation as a variable.
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171
• Store polar equations.
• Select or deselect polar equations.
• Store values directly to window variables.
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Exploring Polar Graphs
Free-Moving Cursor
The free-moving cursor in Pol graphing works the same as in Func
graphing. In RectGC format, moving the cursor updates the values of X
and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC
format, X, Y, R, and q are updated; if CoordOn format is selected, R and q
are displayed.
TRACE
To activate TRACE, press r. When TRACE is active, you can move the
trace cursor along the graph of the equation one qstep at a time. When
you begin a trace, the trace cursor is on the first selected function at
qmin. If ExprOn format is selected, then the equation is displayed.
In RectGC format, TRACE updates the values of X, Y, and q; if CoordOn
format is selected, X, Y, and q are displayed. In PolarGC format, TRACE
updates X, Y, R, and q; if CoordOn format is selected, R and q are
displayed.
To move five plotted points at a time on a function, press y | or
y ~. If you move the trace cursor beyond the top or bottom of the
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screen, the coordinate values at the bottom of the screen continue to
change appropriately.
Quick Zoom is available in Pol graphing mode; panning is not (Chapter 3).
Moving the Trace Cursor to Any Valid q Value
To move the trace cursor to any valid q value on the current function,
enter the number. When you enter the first digit, a q= prompt and the
number you entered are displayed in the bottom-left corner of the
screen. You can enter an expression at the q= prompt. The value must
be valid for the current viewing window. When you complete the entry,
press Í to move the cursor.
ZOOM
ZOOM operations in Pol graphing work the same as in Func graphing.
Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window
variables are affected.
The q window variables (qmin, qmax, and qstep) are not affected, except
when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items
4:Zqmin, 5:Zqmax, and 6:Zqstep are zoom memory variables for Pol
graphing.
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174
Chapter 6:
Sequence Graphing
Getting Started: Forest and Trees
Getting Started is a fast-paced introduction. Read the chapter for details.
A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of
the trees will be harvested and 1,000 new trees will be planted. Will the forest
eventually disappear? Will the forest size stabilize? If so, in how many years and
with how many trees?
1. Press z. Press † † † ~ ~ ~ Í to
select Seq graphing mode.
2. Press y . and select Time axes format
and ExprOn format if necessary.
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3. Press o. If the graph-style icon is not í (dot),
press | |, press Í until í is displayed,
and then press ~ ~.
4. Press ~ 3 to select iPart( (integer part)
because only whole trees are harvested. After
each annual harvest, 80 percent (.80) of the
trees remain.
Press Ë 8 y [u] £ „ ¹ 1 ¤ to define
the number of trees after each harvest. Press
à 1000 ¤ to define the new trees. Press †
4000 to define the number of trees at the
beginning of the program.
5. Press p 0 to set nMin=0. Press † 50 to
set nMax=50. nMin and nMax evaluate forest
size over 50 years. Set the other window
variables.
PlotStart=1
PlotStep=1
Xmin=0
Xmax=50
Xscl=10
Ymin=0
Ymax=6000
Yscl=1000
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6. Press r. Tracing begins at nMin (the start
of the forestry plan). Press ~ to trace the
sequence year by year. The sequence is
displayed at the top of the screen. The values
for n (number of years), X (X=n, because n is
plotted on the x-axis), and Y (tree count) are
displayed at the bottom. When will the forest
stabilize? With how many trees?
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Defining and Displaying Sequence Graphs
TI-83 Plus Graphing Mode Similarities
The steps for defining a sequence graph are similar to the steps for
defining a function graph. Chapter 6 assumes that you are familiar with
Chapter 3: Function Graphing. Chapter 6 details aspects of sequence
graphing that differ from function graphing.
Setting Sequence Graphing Mode
To display the mode screen, press z. To graph sequence functions,
you must select Seq graphing mode before you enter window variables
and before you enter sequence functions.
Sequence graphs automatically plot in Simul mode, regardless of the
current plotting-order mode setting.
TI-83 Plus Sequence Functions u, v, and w
The TI-83 Plus has three sequence functions that you can enter from the
keyboard: u, v, and w. They are above the ¬, −, and ® keys.
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You can define sequence functions in terms of:
• The independent variable n
• The previous term in the sequence function, such as u(nN1)
• The term that precedes the previous term in the sequence function,
such as u(nN2)
• The previous term or the term that precedes the previous term in
another sequence function, such as u(nN1) or u(nN2) referenced in the
sequence v(n).
Note: Statements in this chapter about u(n) are also true for v(n) and w(n);
statements about u(nN1) are also true for v(nN1) and w(nN1); statements about
u(nN2) are also true for v(nN2) and w(nN2).
Displaying the Sequence Y= Editor
After selecting Seq mode, press o to display the sequence Y= editor.
In this editor, you can display and enter sequences for u(n), v(n), and
w(n). Also, you can edit the value for nMin, which is the sequence
window variable that defines the minimum n value to evaluate.
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The sequence Y= editor displays the nMin value because of its relevance
to u(nMin), v(nMin), and w(nMin), which are the initial values for the
sequence equations u(n), v(n), and w(n), respectively.
nMin in the Y= editor is the same as nMin in the window editor. If you
enter a new value for nMin in one editor, the new value for nMin is
updated in both editors.
Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which
requires an initial value.
Selecting Graph Styles
The icons to the left of u(n), v(n), and w(n) represent the graph style of
each sequence (Chapter 3). The default in Seq mode is í (dot), which
shows discrete values. Dot, ç (line), and è (thick) styles are available for
sequence graphing. Graph styles are ignored in Web format.
Selecting and Deselecting Sequence Functions
The TI-83 Plus graphs only the selected sequence functions. In the Y=
editor, a sequence function is selected when the = signs of both u(n)=
and u(nMin)= are highlighted.
To change the selection status of a sequence function, move the cursor
onto the = sign of the function name, and then press Í. The status is
changed for both the sequence function u(n) and its initial value u(nMin).
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Defining and Editing a Sequence Function
To define or edit a sequence function, follow the steps in Chapter 3 for
defining a function. The independent variable in a sequence is n.
In Seq graphing mode, you can enter the sequence variable in either of
two ways.
• Press „.
• Press y N [N].
You can enter the function name from the keyboard.
• To enter the function name u, press y [u] (above ¬).
• To enter the function name v, press y [v] (above −).
• To enter the function name w, press y [w] (above ®).
Generally, sequences are either nonrecursive or recursive. Sequences
are evaluated only at consecutive integer values. n is always a series of
consecutive integers, starting at zero or any positive integer.
Nonrecursive Sequences
In a nonrecursive sequence, the nth term is a function of the
independent variable n. Each term is independent of all other terms.
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For example, in the nonrecursive sequence below, you can calculate u(5)
directly, without first calculating u(1) or any previous term.
The sequence equation above returns the sequence 2, 4, 6, 8, 10, …for
n = 1, 2, 3, 4, 5, … .
Note: You may leave blank the initial value u(nMin) when calculating
nonrecursive sequences.
Recursive Sequences
In a recursive sequence, the nth term in the sequence is defined in
relation to the previous term or the term that precedes the previous term,
represented by u(nN1) and u(nN2). A recursive sequence may also be
defined in relation to n, as in u(n)=u(nN1)+n.
For example, in the sequence below you cannot calculate u(5) without
first calculating u(1), u(2), u(3), and u(4).
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Using an initial value u(nMin) = 1, the sequence above returns
1, 2, 4, 8, 16, . . .
Tip: On the TI-83 Plus, you must type each character of the terms. For
example, to enter u(nN1), press y [u] £ „ ¹ À ¤.
Recursive sequences require an initial value or values, since they
reference undefined terms.
• If each term in the sequence is defined in relation to the previous
term, as in u(nN1), you must specify an initial value for the first term.
• If each term in the sequence is defined in relation to the term that
precedes the previous term, as in u(nN2), you must specify initial
values for the first two terms. Enter the initial values as a list enclosed
in braces ({ }) with commas separating the values.
The value of the first term is 0 and the value of the second term is 1 for
the sequence u(n).
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Setting Window Variables
To display the window variables, press p. These variables define
the viewing window. The values below are defaults for Seq graphing in
both Radian and Degree angle modes.
nMin=1
Smallest n value to evaluate
nMax=10
PlotStart=1
PlotStep=1
Xmin=L10
Xmax=10
Xscl=1
Largest n value to evaluate
First term number to be plotted
Incremental n value (for graphing only)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Ymin=L10
Ymax=10
Yscl=1
nMin must be an integer ‚ 0. nMax, PlotStart, and PlotStep must be
integers ‚ 1.
nMin is the smallest n value to evaluate. nMin also is displayed in the
sequence Y= editor. nMax is the largest n value to evaluate. Sequences
are evaluated at u(nMin), u(nMin+1), u(nMin+2) , . . . , u(nMax).
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185
PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the
first term in the sequence. If you want plotting to begin with the fifth term
in a sequence, for example, set PlotStart=5. The first four terms are
evaluated but are not plotted on the graph.
PlotStep is the incremental n value for graphing only. PlotStep does not
affect sequence evaluation; it only designates which points are plotted
on the graph. If you specify PlotStep=2, the sequence is evaluated at
each consecutive integer, but it is plotted on the graph only at every
other integer.
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186
Selecting Axes Combinations
Setting the Graph Format
To display the current graph format settings, press y .. Chapter
3 describes the format settings in detail. The other graphing modes
share these format settings. The axes setting on the top line of the
screen is available only in Seq mode.
Time Webuv vw uw
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Type of sequence plot (axes)
Rectangular or polar output
Cursor coordinate display on/off
Grid display off or on
Axes display on or off
Axes label display off or on
Expression display on or off
Setting Axes Format
For sequence graphing, you can select from five axes formats. The table
below shows the values that are plotted on the x-axis and y-axis for each
axes setting.
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187
Axes Setting
Time
uv
x-axis
y-axis
u(n), v(n), w(n)
u(n), v(n), w(n)
v(n)
n
u(nN1), v(nN1), w(nN1)
u(n)
v(n)
u(n)
w(n)
uw
w(n)
Displaying a Sequence Graph
To plot the selected sequence functions, press s. As a graph is
plotted, the TI-83 Plus updates X, Y, and n.
Smart Graph applies to sequence graphs (Chapter 3).
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188
Exploring Sequence Graphs
Free-Moving Cursor
The free-moving cursor in Seq graphing works the same as in Func
graphing. In RectGC format, moving the cursor updates the values of X
and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC
format, X, Y, R, and q are updated; if CoordOn format is selected, R and q
are displayed.
TRACE
The axes format setting affects TRACE.
When Time, uv, vw, or uw axes format is selected, TRACE moves the
cursor along the sequence one PlotStep increment at a time. To move
five plotted points at once, press y ~ or y |.
• When you begin a trace, the trace cursor is on the first selected
sequence at the term number specified by PlotStart, even if it is
outside the viewing window.
• Quick Zoom applies to all directions. To center the viewing window
on the current cursor location after you have moved the trace cursor,
press Í. The trace cursor returns to nMin.
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In Web format, the trail of the cursor helps identify points with attracting
and repelling behavior in the sequence. When you begin a trace, the
cursor is on the x-axis at the initial value of the first selected function.
Tip: To move the cursor to a specified n during a trace, enter a value for n, and
press Í. For example, to quickly return the cursor to the beginning of the
sequence, paste nMin to the n= prompt and press Í.
Moving the Trace Cursor to Any Valid n Value
To move the trace cursor to any valid n value on the current function,
enter the number. When you enter the first digit, an n = prompt and the
number you entered are displayed in the bottom-left corner of the
screen. You can enter an expression at the n = prompt. The value must
be valid for the current viewing window. When you have completed the
entry, press Í to move the cursor.
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190
ZOOM
ZOOM operations in Seq graphing work the same as in Func graphing.
Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window
variables are affected.
PlotStart, PlotStep, nMin, and nMax are only affected when you select
ZStandard. The VARS Zoom secondary menu ZU items 1 through 7 are the
ZOOM MEMORY variables for Seq graphing.
CALC
The only CALC operation available in Seq graphing is value.
• When Time axes format is selected, value displays Y (the u(n) value)
for a specified n value.
• When Web axes format is selected, value draws the web and displays
Y (the u(n) value) for a specified n value.
• When uv, vw, or uw axes format is selected, value displays X and Y
according to the axes format setting. For example, for uv axes format,
X represents u(n) and Y represents v(n).
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191
Evaluating u, v, and w
To enter the sequence names u, v, or w, press y [u], [v], or [w]. You can
evaluate these names in any of three ways.
• Calculate the nth value in a sequence.
• Calculate a list of values in a sequence.
• Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional;
default is 1.
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Graphing Web Plots
Graphing a Web Plot
To select Web axes format, press y . ~ Í. A web plot
graphs u(n) versus u(nN1), which you can use to study long-term
behavior (convergence, divergence, or oscillation) of a recursive
sequence. You can see how the sequence may change behavior as its
initial value changes.
Valid Functions for Web Plots
When Web axes format is selected, a sequence will not graph properly or
will generate an error.
• It must be recursive with only one recursion level (u(nN1) but not
u(nN2)).
• It cannot reference n directly.
• It cannot reference any defined sequence except itself.
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193
Displaying the Graph Screen
In Web format, press s to display the graph screen. The TI-83 Plus:
• Draws a y=x reference line in AxesOn format.
• Plots the selected sequences with u(nN1) as the independent
variable.
Note: A potential convergence point occurs whenever a sequence intersects
the y=x reference line. However, the sequence may or may not actually
converge at that point, depending on the sequence’s initial value.
Drawing the Web
To activate the trace cursor, press r. The screen displays the
sequence and the current n, X, and Y values (X represents u(nN1) and Y
represents u(n)). Press ~ repeatedly to draw the web step by step,
starting at nMin. In Web format, the trace cursor follows this course.
1. It starts on the x-axis at the initial value u(nMin) (when PlotStart=1).
2. It moves vertically (up or down) to the sequence.
3. It moves horizontally to the y=x reference line.
4. It repeats this vertical and horizontal movement as you continue to
press ~.
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194
Using Web Plots to Illustrate Convergence
Example: Convergence
1. Press o in Seq mode to display the sequence Y= editor. Make sure
the graph style is set to í (dot), and then define nMin, u(n) and u(nMin)
as shown below.
2. Press y . Í to set Time axes format.
3. Press p and set the variables as shown below.
nMin=1
Xmin=0
Xmax=25
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
nMax=25
PlotStart=1
PlotStep=1
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195
4. Press s to graph the sequence.
5. Press y . and select the Web axes setting.
6. Press p and change the variables below.
Xmin=L10
Xmax=10
7. Press s to graph the sequence.
8. Press r, and then press ~ to draw the web. The displayed cursor
coordinates n, X (u(nN1)), and
Y (u(n)) change accordingly. When you press ~, a new n value is
displayed, and the trace cursor is on the sequence. When you press ~
again, the n value remains the same, and the cursor moves to the y=x
reference line. This pattern repeats as you trace the web.
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Graphing Phase Plots
Graphing with uv, vw, and uw
The phase-plot axes settings uv, vw, and uw show relationships between
two sequences. To select a phase-plot axes setting, press y .,
press ~ until the cursor is on uv, vw, or uw, and then press Í.
Axes Setting
x-axis
u(n)
v(n)
u(n)
y-axis
v(n)
uv
vw
uw
w(n)
w(n)
Example: Predator-Prey Model
Use the predator-prey model to determine the regional populations of a
predator and its prey that would maintain population equilibrium for the
two species.
This example uses the model to determine the equilibrium populations of
foxes and rabbits, with initial populations of 200 rabbits (u(nMin)) and 50
foxes (v(nMin)).
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197
These are the variables (given values are in parentheses):
R = number of rabbits
M = rabbit population growth rate without foxes
K = rabbit population death rate with foxes
W = number of foxes
(.05)
(.001)
G = fox population growth rate with rabbits
D = fox population death rate without rabbits
(.0002)
(.03)
n
= time (in months)
R = R (1+MNKW )
nN1
n
nN1
W = W
(1+GR
ND)
nN1
n
nN1
1. Press o in Seq mode to display the sequence Y= editor. Define the
sequences and initial values for Rn and Wn as shown below. Enter
the sequence Rn as u(n) and enter the sequence Wn as v(n).
2. Press y . Í to select Time axes format.
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198
3. Press p and set the variables as shown below.
nMin=0
Xmin=0
Ymin=0
nMax=400
PlotStart=1
PlotStep=1
Xmax=400
Xscl=100
Ymax=300
Yscl=100
4. Press s to graph the sequence.
5. Press r ~ to individually trace the number of rabbits (u(n)) and
foxes (v(n)) over time (n).
Tip: Press a number, and then press Í to jump to a specific n value
(month) while in TRACE.
6. Press y . ~ ~ Í to select uv axes format.
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7. Press p and change these variables as shown below.
Xmin=84
Xmax=237
Xscl=50
Ymin=25
Ymax=75
Yscl=10
8. Press r. Trace both the number of rabbits (X) and the number of
foxes (Y) through 400 generations.
Note: When you press r, the equation
for u is displayed in the top-left corner. Press
} or † to see the equation for v.
TI-83 Plus
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200
Comparing TI-83 Plus and TI-82 Sequence
Variables
Sequences and Window Variables
Refer to the table if you are familiar with the TI-82. It shows TI-83 Plus
sequences and sequence window variables, as well as their TI-82
counterparts.
TI-83 Plus
In the Y= editor:
u(n)
TI.82
Un
u(nMin)
v(n)
UnStart (window variable)
Vn
v(nMin)
w(n)
VnStart (window variable)
not available
w(nMin)
In the window editor:
nMin
not available
nStart
nMax
nMax
PlotStart
PlotStep
nMin
not available
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Keystroke Differences Between TI-83 Plus
and TI-82
Sequence Keystroke Changes
Refer to the table if you are familiar with the TI-82. It compares
TI-83 Plus sequence-name syntax and variable syntax with TI.82
sequence-name syntax and variable syntax.
TI-83 Plus / TI-82
n / n
On TI-83 Plus, press:
On TI-82, press:
y [n]
„
u(n) / Un
y [u]
y ó ¶ À
£ „ ¤
v(n) / Vn
y [v]
£ „ ¤
y ó ¶ Á
not available
y õ
w(n)
y [w]
£ „ ¤
u(nN1) / UnN1
v(nN1) / VnN1
w(nN1)
y [u]
£ „ ¹ À ¤
y [v]
£ „ ¹ À ¤
y ö
y [w]
not available
£ „ ¹ À ¤
TI-83 Plus
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202
Chapter 7:
Tables
Getting Started: Roots of a Function
Getting Started is a fast-paced introduction. Read the chapter for details.
3
Evaluate the function Y = X N 2X at each integer between L10 and 10. How many
sign changes occur, and at what X values?
1. Press z † † † Í to set Func graphing
mode.
2. Press o. Press „ 3 to select 3.
Then press ¹ 2 „ to enter the function
3
Y1=X N2X.
3. Press y - to display the TABLE SETUP
screen. Press Ì 10 Í to set TblStart=L10.
Press 1 Í to set @Tbl=1.
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203
Press Í to select Indpnt: Auto
(automatically generated independent values).
Press † Í to select Depend: Auto
(automatically generated dependent values).
4. Press y 0 to display the table screen.
5. Press † until you see the sign changes in the
value of Y1. How many sign changes occur, and
at what X values?
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204
Setting Up the Table
TABLE SETUP Screen
To display the TABLE SETUP screen, press y -.
TblStart, @Tbl
TblStart (table start) defines the initial value for the independent variable.
TblStart applies only when the independent variable is generated
automatically (when Indpnt: Auto is selected).
@Tbl (table step) defines the increment for the independent variable.
Note: In Seq mode, both TblStart and @Tbl must be integers.
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205
Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask
Selections
Table Characteristics
Indpnt: Auto
Depend: Auto
Values are displayed automatically in both the
independent-variable column and in all dependent-
variable columns.
Indpnt: Ask
Depend: Auto
The table is empty; when you enter a value for the
independent variable, all corresponding dependent-
variable values are calculated and displayed
automatically.
Indpnt: Auto
Depend: Ask
Values are displayed automatically for the independent
variable; to generate a value for a dependent variable,
move the cursor to that cell and press Í.
Indpnt: Ask
Depend: Ask
The table is empty; enter values for the independent
variable; to generate a value for a dependent variable,
move the cursor to that cell and press Í.
Setting Up the Table from the Home Screen or a Program
To store a value to TblStart, @Tbl, or TblZnput from the home screen or a
program, select the variable name from the VARS TABLE secondary menu.
TblZnput is a list of independent-variable values in the current table.
When you press y - in the program editor, you can select
IndpntAuto, IndpntAsk, DependAuto, and DependAsk.
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Tables
206
Defining the Dependent Variables
Defining Dependent Variables from the Y= Editor
In the Y= editor, enter the functions that define the dependent variables.
Only functions that are selected in the Y= editor are displayed in the
table. The current graphing mode is used. In Par mode, you must define
both components of each parametric equation (Chapter 4).
Editing Dependent Variables from the Table Editor
To edit a selected Y= function from the table editor, follow these steps.
1. Press y 0 to display the table, then press ~ or | to move the
cursor to a dependent-variable column.
2. Press } until the cursor is on the function name at the top of the
column. The function is displayed on the bottom line.
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207
3. Press Í. The cursor moves to the bottom line. Edit the function.
4. Press Í or †. The new values are calculated. The table and the
Y= function are updated automatically.
Note: You also can use this feature to view the function that defines a
dependent variable without having to leave the table.
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208
Displaying the Table
The Table
To display the table, press y 0.
Current cell
Dependent-variable
values in the second
and third columns
Independent-variable
values in the first column
Current cell’s full value
Note: The table abbreviates the values, if necessary.
Independent and Dependent Variables
The current graphing mode determines which independent and
dependent variables are displayed in the table (Chapter 1). In the table
above, for example, the independent variable X and the dependent
variables Y1 and Y2 are displayed because Func graphing mode is set.
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Tables
209
Graphing Mode
Func (function)
Par (parametric)
Pol (polar)
Independent Variable
Dependent Variable
X
T
q
Y1 through Y9, and Y0
X1T/Y1T through X6T/Y6T
r1 through r6
Seq (sequence)
n
u(n), v(n), and w(n)
Clearing the Table from the Home Screen or a Program
From the home screen, select the ClrTable instruction from the CATALOG.
To clear the table, press Í.
From a program, select 9:ClrTable from the PRGM I/O menu or from the
CATALOG. The table is cleared upon execution. If IndpntAsk is selected,
all independent and dependent variable values on the table are cleared.
If DependAsk is selected, all dependent variable values on the table are
cleared.
Scrolling Independent-Variable Values
If Indpnt: Auto is selected, you can press } and † in the independent-
variable column to display more values. As you scroll the column, the
corresponding dependent-variable values also are displayed. All
dependent-variable values may not be displayed if Depend: Ask is
selected.
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210
Note: You can scroll back from the value entered for TblStart. As you scroll,
TblStart is updated automatically to the value shown on the top line of the table.
In the example above, TblStart=0 and @Tbl=1 generates and displays values of
X=0, …, 6; but you can press } to scroll back and display the table for X=M1, …, 5.
Displaying Other Dependent Variables
If you have defined more than two dependent variables, the first two
selected Y= functions are displayed initially. Press ~ or | to display
dependent variables defined by other selected Y= functions. The
independent variable always remains in the left column, except during a
trace with Par graphing mode and G.T split-screen mode set.
Tip: To simultaneously display two dependent variables on the table that are not
defined as consecutive Y= functions, go to the Y= editor and deselect the Y=
functions between the two you want to display. For example, to simultaneously
display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6.
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211
Chapter 8:
Draw Instructions
Getting Started: Drawing a Tangent Line
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to find the equation of the tangent line at X = ‡2/2 for the
function Y = sin(X).
Before you begin, select Radian and Func mode
from the mode screen, if necessary.
1. Press o to display the Y= editor. Press ˜
„ ¤ to store sin(X) in Y1.
2. Press q 7 to select 7:ZTrig, which graphs
the equation in the Zoom Trig window.
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212
3. Press y < 5 to select 5:Tangent(. The
tangent instruction is initiated.
4. Press y C 2 ¤ ¥ 2.
5. Press Í. The tangent line is drawn; the X
value and the tangent-line equation are
displayed on the graph.
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213
Using the DRAW Menu
DRAW Menu
To display the DRAW menu, press y <. The TI-83 Plus’s
interpretation of these instructions depends on whether you accessed
the menu from the home screen or the program editor or directly from a
graph.
DRAW POINTS STO
1:ClrDraw
2:Line(
Clears all drawn elements.
Draws a line segment between 2 points.
Draws a horizontal line.
Draws a vertical line.
Draws a line segment tangent to a function.
Draws a function.
3:Horizontal
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:DrawInv
9:Circle(
0:Text(
Shades an area between two functions.
Draws the inverse of a function.
Draws a circle.
Draws text on a graph screen.
Activates the free-form drawing tool.
A:Pen
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214
Before Drawing on a Graph
The DRAW instructions draw on top of graphs. Therefore, before you use
the DRAW instructions, consider whether you want to perform one or more
of the following actions.
• Change the mode settings on the mode screen.
• Change the format settings on the format screen.
• Enter or edit functions in the Y= editor.
• Select or deselect functions in the Y= editor.
• Change the window variable values.
• Turn stat plots on or off.
• Clear existing drawings with ClrDraw.
Note: If you draw on a graph and then perform any of the actions listed above,
the graph is replotted without the drawings when you display the graph again.
Drawing on a Graph
You can use any DRAW menu instructions except DrawInv to draw on
Func, Par, Pol, and Seq graphs. DrawInv is valid only in Func graphing.
The coordinates for all DRAW instructions are the display’s x-coordinate
and y-coordinate values.
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215
You can use most DRAW menu and DRAW POINTS menu instructions to
draw directly on a graph, using the cursor to identify the coordinates.
You also can execute these instructions from the home screen or from
within a program. If a graph is not displayed when you select a DRAW
menu instruction, the home screen is displayed.
TI-83 Plus
Draw Instructions
216
Clearing Drawings
Clearing Drawings When a Graph Is Displayed
All points, lines, and shading drawn on a graph with DRAW instructions
are temporary.
To clear drawings from the currently displayed graph, select 1:ClrDraw
from the DRAW menu. The current graph is replotted and displayed with
no drawn elements.
Clearing Drawings from the Home Screen or a Program
To clear drawings on a graph from the home screen or a program, begin
on a blank line on the home screen or in the program editor. Select
1:ClrDraw from the DRAW menu. The instruction is copied to the cursor
location. Press Í.
When ClrDraw is executed, it clears all drawings from the current graph
and displays the message Done. When you display the graph again, all
drawn points, lines, circles, and shaded areas will be gone.
Note: Before you clear drawings, you can store them with StorePic.
TI-83 Plus
Draw Instructions
217
Drawing Line Segments
Drawing a Line Segment Directly on a Graph
To draw a line segment when a graph is displayed, follow these steps.
1. Select 2:Line( from the DRAW menu.
2. Place the cursor on the point where you want the line segment to
begin, and then press Í.
3. Move the cursor to the point where you want the line segment to end.
The line is displayed as you move the cursor. Press Í.
To continue drawing line segments, repeat steps 2 and 3. To cancel
Line(, press ‘.
TI-83 Plus
Draw Instructions
218
Drawing Horizontal and Vertical Lines
Drawing a Line Directly on a Graph
To draw a horizontal or vertical line when a graph is displayed, follow
these steps.
1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is
displayed that moves as you move the cursor.
2. Place the cursor on the y-coordinate (for horizontal lines) or
x-coordinate (for vertical lines) through which you want the drawn line
to pass.
3. Press Í to draw the line on the graph.
To continue drawing lines, repeat steps 2 and 3.
To cancel Horizontal or Vertical, press ‘.
TI-83 Plus
Draw Instructions
220
Drawing a Line from the Home Screen or a Program
Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an
expression but not a list.
Horizontal y
Vertical (vertical line) draws a vertical line at X=x. x can be an expression
but not a list.
Vertical x
To instruct the TI-83 Plus to draw more than one horizontal or vertical
line, separate each instruction with a colon ( : ).
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Draw Instructions
221
Drawing Tangent Lines
Drawing a Tangent Line Directly on a Graph
To draw a tangent line when a graph is displayed, follow these steps.
1. Select 5:Tangent( from the DRAW menu.
2. Press † and } to move the cursor to the function for which you want
to draw the tangent line. The current graph’s Y= function is displayed
in the top-left corner, if ExprOn is selected.
3. Press ~ and | or enter a number to select the point on the function at
which you want to draw the tangent line.
4. Press Í. In Func mode, the X value at which the tangent line was
drawn is displayed on the bottom of the screen, along with the
equation of the tangent line. In all other modes, the dy/dx value is
displayed.
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222
Tip: Change the fixed decimal setting on the mode screen if you want to see
fewer digits displayed for X and the equation for Y.
Drawing a Tangent Line from the Home Screen or a Program
Tangent( (tangent line) draws a line tangent to expression in terms of X,
2
such as Y1 or X , at point X=value. X can be an expression. expression is
interpreted as being in Func mode.
Tangent(expression,value)
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Draw Instructions
223
Drawing Functions and Inverses
Drawing a Function
DrawF (draw function) draws expression as a function in terms of X on the
current graph. When you select 6:DrawF from the DRAW menu, the
TI-83 Plus returns to the home screen or the program editor. DrawF is not
interactive.
DrawF expression
Note: You cannot use a list in expression to draw a family of curves.
Drawing an Inverse of a Function
DrawInv (draw inverse) draws the inverse of expression by plotting X values
on the y-axis and Y values on the x-axis. When you select 8:DrawInv from
the DRAW menu, the TI-83 Plus returns to the home screen or the
program editor. DrawInv is not interactive. DrawInv works in Func mode
only.
TI-83 Plus
Draw Instructions
224
DrawInv expression
Note: You cannot use a list in expression to draw a family of curves.
TI-83 Plus
Draw Instructions
225
Shading Areas on a Graph
Shading a Graph
To shade an area on a graph, select 7:Shade( from the DRAW menu. The
instruction is pasted to the home screen or to the program editor.
Shade( draws lowerfunc and upperfunc in terms of X on the current graph
and shades the area that is specifically above lowerfunc and below
upperfunc. Only the areas where lowerfunc < upperfunc are shaded.
Xleft and Xright, if included, specify left and right boundaries for the
shading. Xleft and Xright must be numbers between Xmin and Xmax,
which are the defaults.
pattern specifies one of four shading patterns.
pattern=1
pattern=2
pattern=3
pattern=4
vertical (default)
horizontal
negative—slope 45¡
positive—slope 45¡
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Draw Instructions
226
patres specifies one of eight shading resolutions.
patres=1
patres=2
patres=3
patres=4
patres=5
patres=6
patres=7
patres=8
shades every pixel (default)
shades every second pixel
shades every third pixel
shades every fourth pixel
shades every fifth pixel
shades every sixth pixel
shades every seventh pixel
shades every eighth pixel
Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres])
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Draw Instructions
227
Drawing Circles
Drawing a Circle Directly on a Graph
To draw a circle directly on a displayed graph using the cursor, follow
these steps.
1. Select 9:Circle( from the DRAW menu.
2. Place the cursor at the center of the circle you want to draw. Press
Í.
3. Move the cursor to a point on the circumference. Press Í to draw
the circle on the graph.
Note: This circle is displayed as circular, regardless of the window variable
values, because you drew it directly on the display. When you use the Circle(
instruction from the home screen or a program, the current window
variables may distort the shape.
TI-83 Plus
Draw Instructions
228
To continue drawing circles, repeat steps 2 and 3. To cancel Circle(,
press ‘.
Drawing a Circle from the Home Screen or a Program
Circle( draws a circle with center (X,Y) and radius. These values can be
expressions.
Circle(X,Y,radius)
Tip: When you use Circle( on the home screen or from a program, the current
window values may distort the drawn circle. Use ZSquare (Chapter 3) before
drawing the circle to adjust the window variables and make the circle circular.
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Placing Text on a Graph
Placing Text Directly on a Graph
To place text on a graph when the graph is displayed, follow these steps.
1. Select 0:Text( from the DRAW menu.
2. Place the cursor where you want the text to begin.
3. Enter the characters. Press ƒ or y 7 to enter letters and
q. You may enter TI-83 Plus functions, variables, and instructions.
The font is proportional, so the exact number of characters you can
place on the graph varies. As you type, the characters are placed on
top of the graph.
To cancel Text(, press ‘.
Placing Text on a Graph from the Home Screen or a Program
Text( places on the current graph the characters comprising value, which
can include TI-83 Plus functions and instructions. The top-left corner of
the first character is at pixel (row,column), where row is an integer between
0 and 57 and column is an integer between 0 and 94. Both row and column
can be expressions.
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Text(row,column,value,value…)
value can be text enclosed in quotation marks ( " ), or it can be an
expression. The TI-83 Plus will evaluate an expression and display the
result with up to 10 characters.
Split Screen
On a Horiz split screen, the maximum value for row is 25. On a G.T split
screen, the maximum value for row is 45, and the maximum value for
column is 46.
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Using Pen to Draw on a Graph
Using Pen to Draw on a Graph
Pen draws directly on a graph only. You cannot execute Pen from the
home screen or a program.
To draw on a displayed graph, follow these steps.
1. Select A:Pen from the DRAW menu.
2. Place the cursor on the point where you want to begin drawing. Press
Í to turn on the pen.
3. Move the cursor. As you move the cursor, you draw on the graph,
shading one pixel at a time.
4. Press Í to turn off the pen.
For example, Pen was used to create the arrow pointing to the local
minimum of the selected function.
Note: To continue drawing on the graph, move the
cursor to a new position where you want to begin
drawing again, and then repeat steps 2, 3, and 4. To
cancel Pen, press ‘.
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Drawing Points on a Graph
DRAW POINTS Menu
To display the DRAW POINTS menu, press y < ~. The TI-83 Plus’s
interpretation of these instructions depends on whether you accessed
this menu from the home screen or the program editor or directly from a
graph.
DRAW POINTS STO
1:Pt-On(
Turns on a point.
2:Pt-Off(
Turns off a point.
3:Pt-Change(
4:Pxl-On(
Toggles a point on or off.
Turns on a pixel.
5:Pxl-Off(
6:Pxl-Change(
7:pxl-Test(
Turns off a pixel.
Toggles a pixel on or off.
Returns 1 if pixel on, 0 if pixel off.
Drawing Points Directly on a Graph with Pt.On(
To draw a point on a graph, follow these steps.
1. Select 1:Pt.On( from the DRAW POINTS menu.
2. Move the cursor to the position where you want to draw the point.
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3. Press Í to draw the point.
To continue drawing points, repeat steps 2 and 3. To cancel Pt.On(,
press ‘.
Erasing Points with Pt.Off(
To erase (turn off) a drawn point on a graph, follow these steps.
1. Select 2:Pt.Off( (point off) from the DRAW POINTS menu.
2. Move the cursor to the point you want to erase.
3. Press Í to erase the point.
To continue erasing points, repeat steps 2 and 3. To cancel Pt.Off(,
press ‘.
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Changing Points with Pt.Change(
To change (toggle on or off) a point on a graph, follow these steps.
1. Select 3:Pt.Change( (point change) from the DRAW POINTS menu.
2. Move the cursor to the point you want to change.
3. Press Í to change the point’s on/off status.
To continue changing points, repeat steps 2 and 3. To cancel Pt.Change(,
press ‘.
Drawing Points from the Home Screen or a Program
Pt.On( (point on) turns on the point at (X=x,Y=y). Pt.Off( turns the point off.
Pt.Change( toggles the point on or off. mark is optional; it determines the
point’s appearance; specify 1, 2, or 3, where:
1 = ¦ (dot; default)
2 = › (box)
3 = + (cross)
Pt.On(x,y[,mark])
Pt.Off(x,y[,mark])
Pt.Change(x,y)
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Note: If you specified mark to turn on a point with Pt.On(, you must specify mark
when you turn off the point with Pt.Off(. Pt.Change( does not have the mark
option.
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Drawing Pixels
TI-83 Plus Pixels
A pixel is a square dot on the TI-83 Plus display. The Pxl. (pixel)
instructions let you turn on, turn off, or reverse a pixel (dot) on the graph
using the cursor. When you select a pixel instruction from the DRAW
POINTS menu, the TI-83 Plus returns to the home screen or the program
editor. The pixel instructions are not interactive.
Turning On and Off Pixels with Pxl.On( and Pxl.Off(
Pxl.On( (pixel on) turns on the pixel at (row,column), where row is an
integer between 0 and 62 and column is an integer between 0 and 94.
Pxl.Off( turns the pixel off. Pxl.Change( toggles the pixel on and off.
Pxl.On(row,column)
Pxl.Off(row,column)
Pxl.Change(row,column)
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Using pxl.Test(
pxl.Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if
the pixel is turned off on the current graph. row must be an integer
between 0 and 62. column must be an integer between 0 and 94.
pxl.Test(row,column)
Split Screen
On a Horiz split screen, the maximum value for row is 30 for Pxl.On(,
Pxl.Off(, Pxl.Change(, and pxl.Test(.
On a G.T split screen, the maximum value for row is 50 and the maximum
value for column is 46 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(.
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Storing Graph Pictures (Pic)
DRAW STO Menu
To display the DRAW STO menu, press y < |. When you select an
instruction from the DRAW STO menu, the TI-83 Plus returns to the home
screen or the program editor. The picture and graph database
instructions are not interactive.
DRAW POINTS STO
1:StorePic
2:RecallPic
3:StoreGDB
4:RecallGDB
Stores the current picture.
Recalls a saved picture.
Stores the current graph database.
Recalls a saved graph database.
Storing a Graph Picture
You can store up to 10 graph pictures, each of which is an image of the
current graph display, in picture variables Pic1 through Pic9, or Pic0.
Later, you can superimpose the stored picture onto a displayed graph
from the home screen or a program.
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A picture includes drawn elements, plotted functions, axes, and tick
marks. The picture does not include axes labels, lower and upper bound
indicators, prompts, or cursor coordinates. Any parts of the display
hidden by these items are stored with the picture.
To store a graph picture, follow these steps.
1. Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the
current cursor location.
2. Enter the number (from 1 to 9, or 0) of the picture variable to which
you want to store the picture. For example, if you enter 3, the
TI-83 Plus will store the picture to Pic3.
Note: You also can select a variable from the PICTURE secondary menu
( 4). The variable is pasted next to StorePic.
3. Press Í to display the current graph and store the picture.
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Recalling Graph Pictures (Pic)
Recalling a Graph Picture
To recall a graph picture, follow these steps.
1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the
current cursor location.
2. Enter the number (from 1 to 9, or 0) of the picture variable from which
you want to recall a picture. For example, if you enter 3, the
TI-83 Plus will recall the picture stored to Pic3.
Note: You also can select a variable from the PICTURE secondary menu
( 4). The variable is pasted next to RecallPic.
3. Press Í to display the current graph with the picture
superimposed on it.
Note: Pictures are drawings. You cannot trace a curve that is part of a picture.
Deleting a Graph Picture
To delete graph pictures from memory, use the MEMORY MANAGEMENT
/DELETE secondary menu (Chapter 18).
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Storing Graph Databases (GDB)
What Is a Graph Database?
A graph database (GDB) contains the set of elements that defines a
particular graph. You can recreate the graph from these elements. You
can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and
recall them to recreate graphs.
A GDB stores five elements of a graph.
• Graphing mode
• Window variables
• Format settings
• All functions in the Y= editor and the selection status of each
• Graph style for each Y= function
GDBs do not contain drawn items or stat plot definitions.
Storing a Graph Database
To store a graph database, follow these steps.
1. Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to
the current cursor location.
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2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you
want to store the graph database. For example, if you enter 7, the
TI-83 Plus will store the GDB to GDB7.
Note: You also can select a variable from the GDB secondary menu
( 3). The variable is pasted next to StoreGDB.
3. Press Í to store the current database to the specified GDB
variable.
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Recalling Graph Databases (GDB)
Recalling a Graph Database
CAUTION: When you recall a GDB, it replaces all existing Y= functions.
Consider storing the current Y= functions to another database before
recalling a stored GDB.
To recall a graph database, follow these steps.
1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to
the current cursor location.
2. Enter the number (from 1 to 9, or 0) of the GDB variable from which
you want to recall a GDB. For example, if you enter 7, the TI-83 Plus
will recall the GDB stored to GDB7.
Note: You also can select a variable from the GDB secondary menu
( 3). The variable is pasted next to RecallGDB.
3. Press Í to replace the current GDB with the recalled GDB. The
new graph is not plotted. The TI-83 Plus changes the graphing mode
automatically, if necessary.
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Chapter 9:
Split Screen
Getting Started: Exploring the Unit Circle
Getting Started is a fast-paced introduction. Read the chapter for details.
Use G.T (graph-table) split-screen mode to explore the unit circle and its
relationship to the numeric values for the commonly used trigonometric angles
of 0°, 30°, 45°, 60°, 90°, and so on.
1. Press z to display the mode screen. Press
† † ~ Í to select Degree mode. Press †
~ Í to select Par (parametric) graphing
mode.
Press † † † † ~ ~ Í to select G.T
(graph-table) split-screen mode.
2. Press y . to display the format screen.
Press † † † † † ~ Í to select ExprOff.
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3. Press o to display the Y= editor for Par
graphing mode. Press ™ „ ¤ Í to
store cos(T) to X1T. Press ˜ „ ¤ Í
to store sin(T) to Y1T.
4. Press p to display the window editor.
Enter these values for the window variables.
Tmin=0
Tmax=360
Tstep=15
Xmin=L2.3
Xmax=2.3
Xscl=1
Ymin=L2.5
Ymax=2.5
Yscl=1
5. Press r. On the left, the unit circle is
graphed parametrically in Degree mode and the
trace cursor is activated. When T=0 (from the
graph trace coordinates), you can see from the
table on the right that the value of X1T (cos(T)) is
1 and Y1T (sin(T)) is 0. Press ~ to move the
cursor to the next 15° angle increment. As you
trace around the circle in steps of 15°, an
approximation of the standard value for each
angle is highlighted in the table.
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Using Split Screen
Setting a Split-Screen Mode
To set a split-screen mode, press z, and then move the cursor to the
bottom line of the mode screen.
• Select Horiz (horizontal) to display the graph screen and another
screen split horizontally.
• Select G.T (graph-table) to display the graph screen and table screen
split vertically.
$
$
The split screen is activated when you press any key that applies to
either half of the split screen.
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Some screens are never displayed as split screens. For example, if you
press z in Horiz or G.T mode, the mode screen is displayed as a full
screen. If you then press a key that displays either half of a split screen,
such as r, the split screen returns.
When you press a key or key combination in either Horiz or G.T mode,
the cursor is placed in the half of the display for which that key applies.
For example, if you press r, the cursor is placed in the half in which
the graph is displayed. If you press y 0, the cursor is placed in the
half in which the table is displayed.
The TI-83 Plus will remain in split-screen mode until you change back to
Full screen mode.
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Horiz (Horizontal) Split Screen
Horiz Mode
In Horiz (horizontal) split-screen mode, a horizontal line splits the screen
into top and bottom halves.
The top half displays the graph.
The bottom half displays any of these editors.
• Home screen (four lines)
•
Y= editor (four lines)
• Stat list editor (two rows)
• Window editor (three settings)
• Table editor (two rows)
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Moving from Half to Half in Horiz Mode
To use the top half of the split screen:
• Press s or r.
• Select a ZOOM or CALC operation.
To use the bottom half of the split screen:
• Press any key or key combination that displays the home screen.
• Press o (Y= editor).
• Press … Í (stat list editor).
• Press p (window editor).
• Press y 0 (table editor).
Full Screens in Horiz Mode
All other screens are displayed as full screens in Horiz split-screen mode.
To return to the Horiz split screen from a full screen when in Horiz mode,
press any key or key combination that displays the graph, home screen,
Y= editor, stat list editor, window editor, or table editor.
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G.T (Graph-Table) Split Screen
G.T Mode
In G.T (graph-table) split-screen mode, a vertical line splits the screen
into left and right halves.
The left half displays the graph.
The right half displays the table.
Moving from Half to Half in G.T Mode
To use the left half of the split screen:
• Press s or r.
• Select a ZOOM or CALC operation.
To use the right half of the split screen, press y 0.
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Using r in G.T Mode
As you move the trace cursor along a graph in the split screen’s left half
in G.T mode, the table on the right half automatically scrolls to match the
current cursor values.
Note: When you trace in Par graphing mode, both components of an equation
(XnT and YnT) are displayed in the two columns of the table. As you trace, the
current value of the independent variable T is displayed on the graph.
Full Screens in G.T Mode
All screens other than the graph and the table are displayed as full
screens in G.T split-screen mode.
To return to the G.T split screen from a full screen when in G.T mode,
press any key or key combination that displays the graph or the table.
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TI-83 Plus Pixels in Horiz and G.T Modes
TI-83 Plus Pixels in Horiz and G.T Modes
Note: Each set of numbers in parentheses above represents the row and
column of a corner pixel, which is turned on.
DRAW POINTS Menu Pixel Instructions
For Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(:
• In Horiz mode, row must be {30; column must be {94.
• In G.T mode, row must be {50; column must be {46.
Pxl.On(row,column)
DRAW Menu Text( Instruction
For the Text( instruction:
• In Horiz mode, row must be {25; column must be {94.
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• In G.T mode, row must be {45; column must be {46.
Text(row,column,"text")
PRGM I/O Menu Output( Instruction
For the Output( instruction:
• In Horiz mode, row must be {4; column must be {16.
• In G.T mode, row must be {8; column must be {16.
Output(row,column,"text")
Setting a Split-Screen Mode from the Home Screen or a Program
To set Horiz or G.T from a program, follow these steps.
1. Press z while the cursor is on a blank line in the program editor.
2. Select Horiz or G.T.
The instruction is pasted to the cursor location. The mode is set when
the instruction is encountered during program execution. It remains in
effect after execution.
Note: You also can paste Horiz or G.T to the home screen or program editor
from the CATALOG (Chapter 15).
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Chapter 10:
Matrices
Getting Started: Systems of Linear
Equations
Getting Started is a fast-paced introduction. Read the chapter for details.
Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83 Plus, you
can solve a system of linear equations by entering the coefficients as elements in
a matrix, and then using rref( to obtain the reduced row-echelon form.
1. Press y >. Press ~ ~ to display the
MATRX EDIT menu. Press 1 to select 1: [A]¸
2. Press 2 Í 4 Í to define a 2×4 matrix.
The rectangular cursor indicates the current
element. Ellipses (...) indicate additional
columns beyond the screen.
3. Press 1 Í to enter the first element. The
rectangular cursor moves to the second column
of the first row.
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4. Press 2 Í 3 Í 3 Í to complete the
first row for X + 2Y + 3Z = 3.
5. Press 2 Í 3 Í 4 Í 3 Í to enter
the second row for 2X + 3Y + 4Z = 3.
6. Press y 5 to return to the home screen. If
necessary, press ‘ to clear the home
screen. Press y > ~ to display the
MATRX MATH menu. Press } to wrap to the end
of the menu. Select B:rref( to copy rref( to the
home screen.
7. Press y > 1 to select 1: [A] from the
MATRX NAMES menu. Press ¤ Í. The
reduced row-echelon form of the matrix is
displayed and stored in Ans.
1X N 1Z = L3 therefore
1Y + 2Z = 3 therefore
X = L3 + Z
Y = 3 N 2Z
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Defining a Matrix
What Is a Matrix?
A matrix is a two-dimensional array. You can display, define, or edit a
matrix in the matrix editor. The TI-83 Plus has 10 matrix variables, [A]
through [J]. You can define a matrix directly in an expression. A matrix,
depending on available memory, may have up to 99 rows or columns.
You can store only real numbers in TI-83 Plus matrices.
Selecting a Matrix
Before you can define or display a matrix in the editor, you first must
select the matrix name. To do so, follow these steps.
1. Press y > | to display the MATRX EDIT menu. The dimensions
of any previously defined matrices are displayed.
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2. Select the matrix you want to define. The MATRX EDIT screen is
displayed.
Accepting or Changing Matrix Dimensions
The dimensions of the matrix (row × column) are displayed on the top line.
The dimensions of a new matrix are 1 ×1. You must accept or change the
dimensions each time you edit a matrix. When you select a matrix to
define, the cursor highlights the row dimension.
• To accept the row dimension, press Í.
• To change the row dimension, enter the number of rows (up to 99),
and then press Í.
The cursor moves to the column dimension, which you must accept or
change the same way you accepted or changed the row dimension.
When you press Í, the rectangular cursor moves to the first matrix
element.
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Viewing and Editing Matrix Elements
Displaying Matrix Elements
After you have set the dimensions of the matrix, you can view the matrix
and enter values for the matrix elements. In a new matrix, all values are
zero.
Select the matrix from the MATRX EDIT menu and enter or accept the
dimensions. The center portion of the matrix editor displays up to seven
rows and three columns of a matrix, showing the values of the elements
in abbreviated form if necessary. The full value of the current element,
which is indicated by the rectangular cursor, is displayed on the bottom
line.
This is an 8 × 4 matrix. Ellipses in the left or right column indicate
additional columns. # or $ in the right column indicate additional rows.
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Deleting a Matrix
To delete matrices from memory, use the MEMORY MANAGEMENT/DELETE
secondary menu (Chapter 18).
Viewing a Matrix
The matrix editor has two contexts, viewing and editing. In viewing
context, you can use the cursor keys to move quickly from one matrix
element to the next. The full value of the highlighted element is displayed
on the bottom line.
Select the matrix from the MATRX EDIT menu, and then enter or accept the
dimensions.
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Viewing-Context Keys
Key
Function
| or ~
† or }
Moves the rectangular cursor within the current row
Moves the rectangular cursor within the current column;
on the top row, } moves the cursor to the column
dimension; on the column dimension, } moves the
cursor to the row dimension
Í
‘
Switches to editing context; activates the edit cursor on
the bottom line
Switches to editing context; clears the value on the
bottom line
Any entry character Switches to editing context; clears the value on the
bottom line; copies the character to the bottom line
y 6
{
Nothing
Nothing
Editing a Matrix Element
In editing context, an edit cursor is active on the bottom line. To edit a
matrix element value, follow these steps.
1. Select the matrix from the MATRX EDIT menu, and then enter or accept
the dimensions.
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2. Press |, }, ~, and † to move the cursor to the matrix element you
want to change.
3. Switch to editing context by pressing Í, ‘, or an entry key.
4. Change the value of the matrix element using the editing-context
keys described below. You may enter an expression, which is
evaluated when you leave editing context.
Note: You can press ‘ Í to restore the value at the rectangular
cursor if you make a mistake.
5. Press Í, }, or † to move to another element.
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Editing-Context Keys
Key
Function
| or ~
† or }
Moves the edit cursor within the value
Stores the value displayed on the bottom line to the
matrix element; switches to viewing context and moves
the rectangular cursor within the column
Í
Stores the value displayed on the bottom line to the
matrix element; switches to viewing context and moves
the rectangular cursor to the next row element
‘
Clears the value on the bottom line
Any entry character Copies the character to the location of the edit cursor on
the bottom line
y 6
{
Activates the insert cursor
Deletes the character under the edit cursor on the bottom
line
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Using Matrices with Expressions
Using a Matrix in an Expression
To use a matrix in an expression, you can do any of the following.
• Copy the name from the MATRX NAMES menu.
• Recall the contents of the matrix into the expression with y K
(Chapter 1).
• Enter the matrix directly (see below).
Entering a Matrix in an Expression
You can enter, edit, and store a matrix in the matrix editor. You also can
enter a matrix directly in an expression.
To enter a matrix in an expression, follow these steps.
1. Press y [ [ ] to indicate the beginning of the matrix.
2. Press y [ [ ] to indicate the beginning of a row.
3. Enter a value, which can be an expression, for each element in the
row. Separate the values with commas.
4. Press y [ ] ] to indicate the end of a row.
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5. Repeat steps 2 through 4 to enter all of the rows.
6. Press y [ ] ] to indicate the end of the matrix.
Note: The closing ]] are not necessary at the end of an expression or
preceding !.
The resulting matrix is displayed in the form:
[[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]]
Any expressions are evaluated when the entry is executed.
Note: The commas that you must enter to separate elements are not
displayed on output.
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Displaying and Copying Matrices
Displaying a Matrix
To display the contents of a matrix on the home screen, select the matrix
from the MATRX NAMES menu, and then press Í.
Ellipses in the left or right column indicate additional columns. # or $ in
the right column indicate additional rows. Press ~, |, †, and } to
scroll the matrix.
Copying One Matrix to Another
To copy a matrix, follow these steps.
1. Press y > to display the MATRX NAMES menu.
2. Select the name of the matrix you want to copy.
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3. Press ¿.
4. Press y > again and select the name of the new matrix to
which you want to copy the existing matrix.
5. Press Í to copy the matrix to the new matrix name.
Accessing a Matrix Element
On the home screen or from within a program, you can store a value to,
or recall a value from, a matrix element. The element must be within the
currently defined matrix dimensions. Select matrix from the MATRX NAMES
menu.
[matrix](row,column)
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Using Math Functions with Matrices
Using Math Functions with Matrices
You can use many of the math functions on the TI-83 Plus keyboard, the
MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices.
However, the dimensions must be appropriate. Each of the functions
below creates a new matrix; the original matrix remains the same.
+ (Add), – (Subtract), ä (Multiply)
To add (Ã) or subtract (¹) matrices, the dimensions must be the same.
The answer is a matrix in which the elements are the sum or difference
of the individual corresponding elements.
matrixA+matrixB
matrixANmatrixB
To multiply (¯) two matrices together, the column dimension of matrixA
must match the row dimension of matrixB.
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matrixAämatrixB
Multiplying a matrix by a value or a value by a matrix returns a matrix in
which each element of matrix is multiplied by value.
matrixävalue
valueämatrix
L (Negation)
Negating a matrix (Ì) returns a matrix in which the sign of every
element is changed (reversed).
Lmatrix
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abs(
abs( (absolute value, MATH NUM menu) returns a matrix containing the
absolute value of each element of matrix.
abs(matrix)
round(
round( (MATH NUM menu) returns a matrix. It rounds every element in
matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded
to 10 digits.
round(matrix[,#decimals])
M1 (Inverse)
Use the L1 function (œ) to invert a matrix (^L1 is not valid). matrix must be
square. The determinant cannot equal zero.
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matrixL1
Powers
To raise a matrix to a power, matrix must be square. You can use 2 (¡),
3 (MATH menu), or ^power (›) for integer power between 0 and 255.
matrix2
matrix3
matrix^power
Relational Operations
To compare two matrices using the relational operations = and ƒ (TEST
menu), they must have the same dimensions. = and ƒ compare matrixA
and matrixB on an element-by-element basis. The other relational
operations are not valid with matrices.
matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any
comparison is false.
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matrixAƒmatrixB returns 1 if at least one comparison is false; it returns 0 if
no comparison is false.
iPart(, fPart(, int(
iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are
on the MATH NUM menu.
iPart( returns a matrix containing the integer part of each element of
matrix.
fPart( returns a matrix containing the fractional part of each element of
matrix.
int( returns a matrix containing the greatest integer of each element of
matrix.
iPart(matrix)
fPart(matrix)
int(matrix)
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Using the MATRX MATH Operations
MATRX MATH Menu
To display the MATRX MATH menu, press y > ~.
NAMES MATH EDIT
1:det(
2:T
Calculates the determinant.
Transposes the matrix.
3:dim(
Returns the matrix dimensions.
Fills all elements with a constant.
Returns the identity matrix.
Returns a random matrix.
Appends two matrices.
4:Fill(
5:identity(
6:randM(
7:augment(
8:Matr4list(
9:List4matr(
0:cumSum(
A:ref(
Stores a matrix to a list.
Stores a list to a matrix.
Returns the cumulative sums of a matrix.
Returns the row-echelon form of a matrix.
Returns the reduced row-echelon form.
Swaps two rows of a matrix.
Adds two rows; stores in the second row.
Multiplies the row by a number.
Multiplies the row, adds to the second row.
B:rref(
C:rowSwap(
D:row+(
E:ärow(
F:ärow+(
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det(
det( (determinant) returns the determinant (a real number) of a square
matrix.
det(matrix)
T (Transpose)
T (transpose) returns a matrix in which each element (row, column) is
swapped with the corresponding element (column, row) of matrix.
matrixT
Accessing Matrix Dimensions with dim(
dim( (dimension) returns a list containing the dimensions ({rows columns})
of matrix.
dim(matrix)
Note: dim(matrix)!Ln:Ln(1) returns the number of rows. dim(matrix)!Ln:Ln(2)
returns the number of columns.
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Creating a Matrix with dim(
Use dim( with ¿ to create a new matrixname of dimensions
rows × columns with 0 as each element.
{rows,columns}!dim(matrixname)
Redimensioning a Matrix with dim(
Use dim( with ¿ to redimension an existing matrixname to dimensions
rows × columns. The elements in the old matrixname that are within the new
dimensions are not changed. Additional created elements are zeros.
Matrix elements that are outside the new dimensions are deleted.
{rows,columns}!dim(matrixname)
Fill(
Fill( stores value to every element in matrixname.
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Fill(value,matrixname)
identity(
identity( returns the identity matrix of dimension rows × dimension columns.
identity(dimension)
randM(
randM( (create random matrix) returns a rows × columns random matrix of
L
integers ‚ 9 and 9. The seed value stored to the rand function controls
the values (Chapter 2).
randM(rows,columns)
augment(
augment( appends matrixA to matrixB as new columns. matrixA and matrixB
both must have the same number of rows.
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augment(matrixA,matrixB)
Matr4list(
Matr4list( (matrix stored to list) fills each listname with elements from each
column in matrix. Matr4list( ignores extra listname arguments. Likewise,
Matr4list( ignores extra matrix columns.
Matr4list(matrix,listnameA,...,listname n)
&
Matr4list( also fills a listname with elements from a specified column# in matrix.
To fill a list with a specific column from matrix, you must enter column# after
matrix.
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Matr4list(matrix,column#,listname)
&
List4matr(
List4matr( (lists stored to matrix) fills matrixname column by column with the
elements from each list. If dimensions of all lists are not equal, List4matr( fills
each extra matrixname row with 0. Complex lists are not valid.
List4matr(listA,...,list n,matrixname)
&
cumSum(
cumSum( returns cumulative sums of the elements in matrix, starting with
the first element. Each element is the cumulative sum of the column from
top to bottom.
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cumSum(matrix)
Row Operations
MATRX MATH menu items A through F are row operations. You can use a
row operation in an expression. Row operations do not change matrix in
memory. You can enter all row numbers and values as expressions. You
can select the matrix from the MATRX NAMES menu.
ref(, rref(
ref( (row-echelon form) returns the row-echelon form of a real matrix. The
number of columns must be greater than or equal to the number of rows.
ref(matrix)
rref( (reduced row-echelon form) returns the reduced row-echelon form of
a real matrix. The number of columns must be greater than or equal to the
number of rows.
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ärow(
ärow( (row multiplication) returns a matrix. It multiplies row of matrix by
value and stores the results in row.
ärow(value,matrix,row)
ärow+(
ärow+( (row multiplication and addition) returns a matrix. It multiplies rowA
of matrix by value, adds it to rowB, and stores the results in rowB.
ärow+(value,matrix,rowA,rowB)
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Chapter 11:
Lists
Getting Started: Generating a Sequence
Getting Started is a fast-paced introduction. Read the chapter for details.
2
Calculate the first eight terms of the sequence 1/A . Store the results to a user-
created list. Then display the results in fraction form. Begin this example on a
blank line on the home screen.
1. Press y 9 ~ to display the LIST OPS menu.
2. Press 5 to select 5:seq(, which pastes seq( to
the current cursor location.
3. Press 1 ¥ ƒ [A] ¡ ¢ ƒ [A] ¢ 1 ¢ 8
¢ 1 ¤ to enter the sequence.
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4. Press ¿, and then press y ƒ to turn
on alpha-lock. Press [S] [E] [Q], and then press
ƒ to turn off alpha-lock. Press 1 to
complete the list name.
5. Press Í to generate the list and store it in
SEQ1. The list is displayed on the home screen.
An ellipsis (...) indicates that the list continues
beyond the viewing window. Press ~
repeatedly (or press and hold ~) to scroll the
list and view all the list elements.
6. Press y 9 to display the LIST NAMES menu.
Press 7 to select 7:seq( to paste ÙSEQ1 to the
current cursor location. (If SEQ1 is not item 7 on
your LIST NAMES menu, move the cursor to SEQ1
before you press Í.)
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7. Press to display the MATH menu. Press 1
to select 1:4Frac, which pastes 4Frac to the
current cursor location.
8. Press Í to show the sequence in fraction
form. Press ~ repeatedly (or press and hold
~) to scroll the list and view all the list
elements.
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Naming Lists
Using TI-83 Plus List Names L1 through L6
The TI-83 Plus has six list names in memory: L1, L2, L3, L4, L5, and L6.
The list names L1 through L6 are on the keyboard above the numeric
keys À through ¸. To paste one of these names to a valid screen, press
y, and then press the appropriate key. L1 through L6 are stored in stat
list editor columns 1 through 6 when you reset memory.
Creating a List Name on the Home Screen
To create a list name on the home screen, follow these steps.
1. Press y E, enter one or more list elements, and then press y F.
Separate list elements with commas. List elements can be real
numbers, complex numbers, or expressions.
2. Press ¿.
3. Press ƒ [letter from A to Z or q] to enter the first letter of the
name.
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4. Enter zero to four letters, q, or numbers to complete the name.
5. Press Í. The list is displayed on the next line. The list name and
its elements are stored in memory. The list name becomes an item
on the LIST NAMES menu.
Note: If you want to view a user-created list in the stat list editor, you must
store it in the stat list editor (Chapter 12).
You also can create a list name in these four places.
• At the Name= prompt in the stat list editor
• At an Xlist:, Ylist:, or Data List: prompt in the stat plot editor
• At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or YList: prompt
in the inferential stat editors
• On the home screen using SetUpEditor
You can create as many list names as your TI-83 Plus memory has
space to store.
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Storing and Displaying Lists
Storing Elements to a List
You can store list elements in either of two ways.
• Use braces and ¿ on the home screen.
• Use the stat list editor (Chapter 12).
The maximum dimension of a list is 999 elements.
Tip: When you store a complex number to a list, the entire list is converted to a
list of complex numbers. To convert the list to a list of real numbers, display the
home screen, and then enter real(listname)!listname.
Displaying a List on the Home Screen
To display the elements of a list on the home screen, enter the name of
indicates that the list continues beyond the viewing window. Press ~
repeatedly (or press and hold ~) to scroll the list and view all the list
elements.
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Copying One List to Another
To copy a list, store it to another list.
Accessing a List Element
You can store a value to or recall a value from a specific list element. You
can store to any element within the current list dimension or one element
beyond.
listname(element)
Deleting a List from Memory
To delete lists from memory, including L1 through L6, use the
MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Resetting
memory restores L1 through L6. Removing a list from the stat list editor
does not delete it from memory.
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Entering List Names
Using the LIST NAMES Menu
To display the LIST NAMES menu, press y 9. Each item is a user-
created list name. LIST NAMES menu items are sorted automatically in
alphanumerical order. Only the first 10 items are labeled, using 1 through
9, then 0. To jump to the first list name that begins with a particular alpha
character or q, press ƒ [letter from A to Z or q].
Tip: From the top of a menu, press } to move to the bottom. From the bottom,
press † to move to the top.
Note: The LIST NAMES menu omits list names L1 through L6. Enter L1 through L6
directly from the keyboard.
When you select a list name from the LIST NAMES menu, the list name is
pasted to the current cursor location.
• The list name symbol Ù precedes a list name when the name is
pasted where non-list name data also is valid, such as the home
screen.
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• The Ù symbol does not precede a list name when the name is pasted
where a list name is the only valid input, such as the stat list editor’s
Name= prompt or the stat plot editor’s XList: and YList: prompts.
Entering a User-Created List Name Directly
To enter an existing list name directly, follow these steps.
1. Press y 9 ~ to display the LIST OPS menu.
always necessary.
Note: You also can paste Ù to the current
cursor location from the CATALOG
(Chapter 15).
3. Enter the characters that comprise the list name.
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Attaching Formulas to List Names
Attaching a Formula to a List Name
You can attach a formula to a list name so that each list element is a
result of the formula. When executed, the attached formula must resolve
to a list.
When anything in the attached formula changes, the list to which the
formula is attached is updated automatically.
• When you edit an element of a list that is referenced in the formula,
the corresponding element in the list to which the formula is attached
is updated.
• When you edit the formula itself, all elements in the list to which the
formula is attached are updated.
For example, the first screen below shows that elements are stored to
L3, and the formula L3+10 is attached to the list name ÙADD10. The
quotation marks designate the formula to be attached to ÙADD10. Each
element of ÙADD10 is the sum of an element in L3 and 10.
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The next screen shows another list, L4. The elements of L4 are the sum
of the same formula that is attached to L3. However, quotation marks are
not entered, so the formula is not attached to L4.
On the next line, L6!L3(1):L3 changes the first element in L3 to L6, and
then redisplays L3.
The last screen shows that editing L3 updated ÙADD10, but did not
change L4. This is because the formula L3+10 is attached to ÙADD10, but
it is not attached to L4.
Note: To view a formula that is attached to a list name, use the stat list editor
(Chapter 12).
Attaching a Formula to a List on the Home Screen or in a Program
To attach a formula to a list name from a blank line on the home screen
or from a program, follow these steps.
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1. Press ƒ [ã], enter the formula (which must resolve to a list), and
press ƒ [ã] again.
Note: When you include more than one list name in a formula, each list
must have the same dimension.
2. Press ¿.
3. Enter the name of the list to which you want to attach the formula.
• Press y, and then enter a TI-83 Plus list name L1 through L6.
• Press y 9 and select a user.created list name from the
LIST NAMES menu.
4. Press Í.
Note: The stat list editor displays a formula-lock symbol next to each list name
that has an attached formula. Chapter 12 describes how to use the stat list
editor to attach formulas to lists, edit attached formulas, and detach formulas
from lists.
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Detaching a Formula from a List
You can detach (clear) an attached formula from a list in several ways.
For example:
• Enter ""!listname on the home screen.
• Edit any element of a list to which a formula is attached.
• Use the stat list editor (Chapter 12).
• Use ClrList or ClrAllList to detach a formula from a list (Chapter 18).
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Using Lists in Expressions
Using a List in an Expression
You can use lists in an expression in any of three ways. When you press
Í, any expression is evaluated for each list element, and a list is
displayed.
• Use L1–L6 or any user-created list name in an expression.
• Enter the list elements directly.
• Use y K to recall the contents of the list into an expression at the
cursor location (Chapter 1).
&
Note: You must paste user-created list names to the Rcl prompt by selecting
them from the LIST NAMES menu. You cannot enter them directly using Ù.
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Using Lists with Math Functions
You can use a list to input several values for some math functions. Other
chapters and Appendix A specify whether a list is valid. The function is
evaluated for each list element, and a list is displayed.
• When you use a list with a function, the function must be valid for
every element in the list. In graphing, an invalid element, such as L1
in ‡({1,0,L1}), is ignored.
This returns an error.
This graphs Xä‡(1) and Xä‡(0),
but skips Xä‡(L1).
• When you use two lists with a two-argument function, the dimension
of each list must be the same. The function is evaluated for
corresponding elements.
• When you use a list and a value with a two-argument function, the
value is used with each element in the list.
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LIST OPS Menu
LIST OPS Menu
To display the LIST OPS menu, press y 9 ~.
NAMES OPS MATH
1:SortA(
2:SortD(
3:dim(
Sorts lists in ascending order.
Sorts lists in descending order.
Sets the list dimension.
4:Fill(
Fills all elements with a constant.
Creates a sequence.
5:seq(
6:cumSum(
7:@List(
8:Select(
9:augment(
0:List4matr(
A:Matr4list(
B:Ù
Returns a list of cumulative sums.
Returns difference of successive elements.
Selects specific data points.
Concatenates two lists.
Stores a list to a matrix.
Stores a matrix to a list.
Designates the list-name data type.
SortA(, SortD(
SortA( (sort ascending) sorts list elements from low to high values.
SortD( (sort descending) sorts list elements from high to low values.
Complex lists are sorted based on magnitude (modulus).
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With one list, SortA( and SortD( sort the elements of listname and update
the list in memory.
SortA(listname)
SortD(listname)
With two or more lists, SortA( and SortD( sort keylistname, and then sort
each dependlist by placing its elements in the same order as the
corresponding elements in keylistname. All lists must have the same
dimension.
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])
SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])
Note: In the example, 5 is the first element in L4, and 1 is the first element in
L5. After SortA(L4,L5), 5 becomes the second element of L4, and likewise, 1
becomes the second element of L5.
Note: SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT
menu (Chapter 12).
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Using dim( to Find List Dimensions
dim( (dimension) returns the length (number of elements) of list.
dim(list)
Using dim( to Create a List
You can use dim( with ¿ to create a new listname with dimension
length from 1 to 999. The elements are zeros.
length!dim(listname)
Using dim( to Redimension a List
You can use dim with ¿ to redimension an existing listname to
dimension length from 1 to 999.
• The elements in the old listname that are within the new dimension are
not changed.
• Extra list elements are filled by 0.
• Elements in the old list that are outside the new dimension are deleted.
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length!dim(listname)
Fill(
Fill( replaces each element in listname with value.
Fill(value,listname)
Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu
(Chapter 10).
seq(
seq( (sequence) returns a list in which each element is the result of the
evaluation of expression with regard to variable for the values ranging from
begin to end at steps of increment. variable need not be defined in memory.
increment can be negative; the default value for increment is 1. seq( is not
valid within expression. Complex lists are not valid.
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seq(expression,variable,begin,end[,increment])
cumSum(
cumSum( (cumulative sum) returns the cumulative sums of the elements
in list, starting with the first element. list elements can be real or complex
numbers.
cumSum(list)
@List(
@List( returns a list containing the differences between consecutive
elements in list. @List subtracts the first element in list from the second
element, subtracts the second element from the third, and so on. The list
of differences is always one element shorter than the original list. list
elements can be a real or complex numbers.
@List(list)
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Select(
Select( selects one or more specific data points from a scatter plot or
xyLine plot (only), and then stores the selected data points to two new
lists, xlistname and ylistname. For example, you can use Select( to select
and then analyze a portion of plotted CBL 2™/CBL™ or CBR™ data.
Select(xlistname,ylistname)
Note: Before you use Select(, you must have selected (turned on) a scatter plot
or xyLine plot. Also, the plot must be displayed in the current viewing window.
Before Using Select(
Before using Select(, follow these steps.
1. Create two list names and enter the data.
2. Turn on a stat plot, select " (scatter plot) or Ó (xyLine), and enter the
two list names for Xlist: and Ylist: (Chapter 12).
3. Use ZoomStat to plot the data (Chapter 3).
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Using Select( to Select Data Points from a Plot
To select data points from a scatter plot or xyLine plot, follow these
steps.
1. Press y 9 ~ 8 to select 8:Select( from the LIST OPS menu. Select(
is pasted to the home screen.
2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to
designate list names into which you want the selected data to be
stored.
3. Press Í. The graph screen is displayed with Left Bound? in the
bottom-left corner.
4. Press } or † (if more than one stat plot is selected) to move the
cursor onto the stat plot from which you want to select data points.
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5. Press | and ~ to move the cursor to the stat plot data point that you
want as the left bound.
6. Press Í. A 4 indicator on the graph screen shows the left bound.
Right Bound? is displayed in the bottom-left corner.
7. Press | or ~ to move the cursor to the stat plot point that you want for
the right bound, and then press Í.
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The x-values and y-values of the selected points are stored in
xlistname and ylistname. A new stat plot of xlistname and ylistname
replaces the stat plot from which you selected data points. The list
names are updated in the stat plot editor.
Note: The two new lists (xlistname and ylistname) will include the points you
select as left bound and right bound. Also, left-bound x-value right-bound x-value
must be true.
augment(
augment( concatenates the elements of listA and listB. The list elements
can be real or complex numbers.
augment(listA,listB)
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List4matr(
List4matr( (lists stored to matrix) fills matrixname column by column with
the elements from each list. If the dimensions of all lists are not equal,
then List4matr( fills each extra matrixname row with 0. Complex lists are
not valid.
List4matr(list1,list2, . . . ,list n,matrixname)
&
Matr4list(
Matr4list( (matrix stored to lists) fills each listname with elements from
each column in matrix. If the number of listname arguments exceeds the
number of columns in matrix, then Matr4list( ignores extra listname
arguments. Likewise, if the number of columns in matrix exceeds the
number of listname arguments, then Matr4list( ignores extra matrix
columns.
Matr4list(matrix,listname1,listname2, . . . ,listname n)
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&
Matr4list( also fills a listname with elements from a specified column# in
matrix. To fill a list with a specific column from matrix, you must enter a
column# after matrix.
Matr4list(matrix,column#,listname)
&
Ù preceding one to five characters identifies those characters as a user-
created listname. listname may comprise letters, q, and numbers, but it
must begin with a letter from A to Z or q.
Ùlistname
Generally, Ù must precede a user-created list name when you enter a
user-created list name where other input is valid, for example, on the
home screen. Without the Ù, the TI-83 Plus may misinterpret a user-
created list name as implied multiplication of two or more characters.
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Ù need not precede a user-created list name where a list name is the
only valid input, for example, at the Name= prompt in the stat list editor or
the Xlist: and Ylist: prompts in the stat plot editor. If you enter Ù where it
is not necessary, the TI-83 Plus will ignore the entry.
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LIST MATH Menu
LIST MATH Menu
To display the LIST MATH menu, press y 9 |.
NAMES OPS MATH
1:min(
Returns minimum element of a list.
Returns maximum element of a list.
Returns mean of a list.
2:max(
3:mean(
4:median(
5:sum(
Returns median of a list.
Returns sum of elements in a list.
Returns product of elements in list.
Returns standard deviation of a list.
Returns the variance of a list.
6:prod(
7:stdDev(
8:variance(
min(, max(
min( (minimum) and max( (maximum) return the smallest or largest
element of listA. If two lists are compared, it returns a list of the smaller or
larger of each pair of elements in listA and listB. For a complex list, the
element with smallest or largest magnitude (modulus) is returned.
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min(listA[,listB])
max(listA[,listB])
Note: min( and max( are the same as min( and max( on the MATH NUM menu.
mean(, median(
mean( returns the mean value of list. median( returns the median value of
list. The default value for freqlist is 1. Each freqlist element counts the
number of consecutive occurrences of the corresponding element in list.
Complex lists are not valid.
mean(list[,freqlist])
median(list[,freqlist])
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sum(, prod(
sum( (summation) returns the sum of the elements in list. start and end are
optional; they specify a range of elements. list elements can be real or
complex numbers.
prod( returns the product of all elements of list. start and end elements are
optional; they specify a range of list elements. list elements can be real
or complex numbers.
sum(list[,start,end])
prod(list[,start,end])
Sums and Products of Numeric Sequences
You can combine sum( or prod( with seq( to obtain:
upper
upper
expression(x)
x=lower
expression(x)
∏
G
x=lower
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313
To evaluate G 2(N–1) from N=1 to 4:
stdDev(, variance(
stdDev( returns the standard deviation of the elements in list. The default
value for freqlist is 1. Each freqlist element counts the number of
consecutive occurrences of the corresponding element in list. Complex lists
are not valid.
variance( returns the variance of the elements in list. The default value for
freqlist is 1. Each freqlist element counts the number of consecutive
occurrences of the corresponding element in list. Complex lists are not
valid.
stdDev(list[,freqlist])
variance(list[,freqlist])
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314
Chapter 12:
Statistics
Getting Started: Pendulum Lengths and
Periods
Getting Started is a fast-paced introduction. Read the chapter for details.
A group of students is attempting to determine the mathematical relationship
between the length of a pendulum and its period (one complete swing of a
pendulum). The group makes a simple pendulum from string and washers and
then suspends it from the ceiling. They record the pendulum’s period for each of
12 string lengths.*
Length (cm)
Time (sec)
Length (cm)
Time (sec)
6.5
0.51
0.68
0.73
0.79
0.88
0.99
24.4
26.6
30.5
34.3
37.6
41.5
1.01
1.08
1.13
1.26
1.28
1.32
11.0
13.2
15.0
18.0
23.1
*This example is quoted and adapted from Contemporary Precalculus Through
Applications, by the North Carolina School of Science and Mathematics, by permission
of Janson Publications, Inc., Dedham, MA. 1-800-322-MATH. © 1992. All rights
reserved.
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315
1. Press z † † † Í to set Func graphing
mode.
2. Press … 5 to select 5:SetUpEditor.
SetUpEditor is pasted to the home screen.
Press Í. This removes lists from stat list
editor columns 1 through 20, and then stores
lists L1 through L6 in columns 1 through 6.
Note: Removing lists from the stat list editor does
not delete them from memory.
3. Press … 1 to select 1:Edit from the STAT
EDIT menu. The stat list editor is displayed.
If elements are stored in L1 and L2, press
} to move the cursor onto L1, and then
press ‘ Í ~ } ‘ Í to
clear both lists. Press | to move the
rectangular cursor back to the first row in
L1.
4. Press 6 Ë 5 Í to store the first pendulum
string length (6.5 cm) in L1. The rectangular
cursor moves to the next row. Repeat this step
to enter each of the 12 string length values in
the table.
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5. Press ~ to move the rectangular cursor to the
first row in L2.
Press Ë 51 Í to store the first time
measurement (.51 sec) in L2. The rectangular
cursor moves to the next row. Repeat this step
to enter each of the 12 time values in the table.
6. Press o to display the Y= editor.
If necessary, press ‘ to clear the function
Y1. As necessary, press }, Í, and ~ to turn
off Plot1, Plot2, and Plot3 from the top line of the
Y= editor (Chapter 3). As necessary, press †, |,
and Í to deselect functions.
7. Press y , 1 to select 1:Plot1 from the
STAT PLOTS menu. The stat plot editor is
displayed for plot 1.
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8. Press Í to select On, which turns on plot 1.
Press † Í to select " (scatter plot). Press
† y d to specify Xlist:L1 for plot 1. Press †
y e to specify Ylist:L2 for plot 1. Press † ~
Í to select + as the Mark for each data point
on the scatter plot.
9. Press q 9 to select 9:ZoomStat from the
ZOOM menu. The window variables are adjusted
automatically, and plot 1 is displayed. This is a
scatter plot of the time-versus-length data.
Since the scatter plot of time-versus-length data appears to be
approximately linear, fit a line to the data.
10. Press … ~ 4 to select 4:LinReg(ax+b) (linear
regression model) from the STAT CALC menu.
LinReg(ax+b) is pasted to the home screen.
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11. Press y d ¢ y e ¢. Press ~ 1 to
display the VARS Y.VARS FUNCTION secondary
menu, and then press 1 to select 1:Y1. L1, L2,
and Y1 are pasted to the home screen as
arguments to LinReg(ax+b).
12. Press Í to execute LinReg(ax+b). The linear
regression for the data in L1 and L2 is calculated.
Values for a and b are displayed on the home
screen. The linear regression equation is stored
in Y1. Residuals are calculated and stored
automatically in the list name RESID, which
becomes an item on the LIST NAMES menu.
13. Press s. The regression line and the
scatter plot are displayed.
The regression line appears to fit the central portion of the scatter plot
well. However, a residual plot may provide more information about this
fit.
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14. Press … 1 to select 1:Edit. The stat list
editor is displayed.
Press ~ and } to move the cursor onto L3.
Press y 6. An unnamed column is
displayed in column 3; L3, L4, L5, and L6 shift
right one column. The Name= prompt is
displayed in the entry line, and alpha-lock is
on.
15. Press y 9 to display the LIST NAMES menu.
If necessary, press † to move the cursor onto
the list name RESID.
16. Press Í to select RESID and paste it to the
stat list editor’s Name= prompt.
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17. Press Í. RESID is stored in column 3 of the
stat list editor.
Press † repeatedly to examine the residuals.
Notice that the first three residuals are negative. They correspond to the
shortest pendulum string lengths in L1. The next five residuals are
positive, and three of the last four are negative. The latter correspond to
the longer string lengths in L1. Plotting the residuals will show this pattern
more clearly.
18. Press y , 2 to select 2:Plot2 from the
STAT PLOTS menu. The stat plot editor is
displayed for plot 2.
19. Press Í to select On, which turns on plot 2.
Press † Í to select " (scatter plot). Press
† y d to specify Xlist:L1 for plot 2. Press †
[R] [E] [S] [I] [D] (alpha-lock is on) to specify
Ylist:RESID for plot 2. Press † Í to select
› as the mark for each data point on the
scatter plot.
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20. Press o to display the Y= editor.
Press | to move the cursor onto the = sign,
and then press Í to deselect Y1. Press }
Í to turn off plot 1.
21. Press q 9 to select 9:ZoomStat from the
ZOOM menu. The window variables are
adjusted automatically, and plot 2 is displayed.
This is a scatter plot of the residuals.
Notice the pattern of the residuals: a group of negative residuals, then a
group of positive residuals, and then another group of negative residuals.
The residual pattern indicates a curvature associated with this data set
for which the linear model did not account. The residual plot emphasizes
a downward curvature, so a model that curves down with the data would
be more accurate. Perhaps a function such as square root would fit. Try
a power regression to fit a function of the form y = a ä xb.
22. Press o to display the Y= editor.
Press ‘ to clear the linear regression
equation from Y1. Press } Í to turn on
plot 1. Press ~ Í to turn off plot 2.
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23. Press q 9 to select 9:ZoomStat from the
ZOOM menu. The window variables are
adjusted automatically, and the original scatter
plot of time-versus-length data (plot 1) is
displayed.
24. Press … ~ ƒ [A] to select A:PwrReg
from the STAT CALC menu. PwrReg is pasted to
the home screen.
Press y d ¢ y e ¢. Press ~ 1 to
display the VARS Y.VARS FUNCTION secondary
menu, and then press 1 to select 1:Y1. L1, L2,
and Y1 are pasted to the home screen as
arguments to PwrReg.
25. Press Í to calculate the power regression.
Values for a and b are displayed on the home
screen. The power regression equation is
stored in Y1. Residuals are calculated and
stored automatically in the list name RESID.
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26. Press s. The regression line and the
scatter plot are displayed.
The new function y=.192x.522 appears to fit the data well. To get more
information, examine a residual plot.
27. Press o to display the Y= editor.
Press | Í to deselect Y1.
Press } Í to turn off plot 1. Press ~
Í to turn on plot 2.
Note: Step 19 defined plot 2 to plot residuals
(RESID) versus string length (L1).
28. Press q 9 to select 9:ZoomStat from the
ZOOM menu. The window variables are
adjusted automatically, and plot 2 is displayed.
This is a scatter plot of the residuals.
The new residual plot shows that the residuals are random in sign, with
the residuals increasing in magnitude as the string length increases.
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To see the magnitudes of the residuals, continue with these steps.
29. Press r.
Press ~ and | to trace the data. Observe the
values for Y at each point.
With this model, the largest positive residual is
about 0.041 and the smallest negative residual
is about L0.027. All other residuals are less
than 0.02 in magnitude.
Now that you have a good model for the relationship between length and
period, you can use the model to predict the period for a given string
length. To predict the periods for a pendulum with string lengths of 20 cm
and 50 cm, continue with these steps.
30. Press ~ 1 to display the VARS Y.VARS
FUNCTION secondary menu, and then press 1 to
select 1:Y1. Y1 is pasted to the home screen.
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31. Press £ 20 ¤ to enter a string length of
20 cm.
Press Í to calculate the predicted time of
about 0.92 seconds.
Based on the residual analysis, we would
expect the prediction of about 0.92 seconds to
be within about 0.02 seconds of the actual
value.
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32. Press y [ to recall the Last Entry.
Press | | | 5 to change the string length to
50 cm.
33. Press Í to calculate the predicted time of
about 1.48 seconds.
Since a string length of 50 cm exceeds the
lengths in the data set, and since residuals
appear to be increasing as string length
increases, we would expect more error with
this estimate.
Note: You also can make predictions using the
table with the TABLE SETUP settings Indpnt:Ask and
Depend:Auto (Chapter 7).
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Setting Up Statistical Analyses
Using Lists to Store Data
Data for statistical analyses is stored in lists, which you can create and
edit using the stat list editor. The TI-83 Plus has six list variables in
memory, L1 through L6, to which you can store data for statistical
calculations. Also, you can store data to list names that you create
(Chapter 11).
Setting Up a Statistical Analysis
To set up a statistical analysis, follow these steps. Read the chapter for
details.
1. Enter the statistical data into one or more lists.
2. Plot the data.
3. Calculate the statistical variables or fit a model to the data.
4. Graph the regression equation for the plotted data.
5. Graph the residuals list for the given regression model.
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Displaying the Stat List Editor
The stat list editor is a table where you can store, edit, and view up to 20
lists that are in memory. Also, you can create list names from the stat list
editor.
To display the stat list editor, press …, and then select 1:Edit from the
STAT EDIT menu.
The top line displays list names. L1 through L6 are stored in columns 1
through 6 after a memory reset. The number of the current column is
displayed in the top-right corner.
The bottom line is the entry line. All data entry occurs on this line. The
characteristics of this line change according to the current context.
The center area displays up to seven elements of up to three lists; it
abbreviates values when necessary. The entry line displays the full value
of the current element.
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Using the Stat List Editor
Entering a List Name in the Stat List Editor
To enter a list name in the stat list editor, follow these steps.
1. Display the Name= prompt in the entry line in either of two ways.
• Move the cursor onto the list name in the column where you want
to insert a list, and then press y 6. An unnamed column is
displayed and the remaining lists shift right one column.
• Press } until the cursor is on the top line, and then press ~ until
you reach the unnamed column.
Note: If list names are stored to all 20 columns, you must remove a list
name to make room for an unnamed column.
The Name= prompt is displayed and alpha-lock is on.
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2. Enter a valid list name in any of four ways.
• Select a name from the LIST NAMES menu (Chapter 11).
• Enter L1, L2, L3, L4, L5, or L6 from the keyboard.
• Enter an existing user-created list name directly from the keyboard.
• Enter a new user-created list name.
3. Press Í or † to store the list name and its elements, if any, in
the current column of the stat list editor.
To begin entering, scrolling, or editing list elements, press †. The
rectangular cursor is displayed.
Note: If the list name you entered in step 2 already was stored in another stat
list editor column, then the list and its elements, if any, move to the current
column from the previous column. Remaining list names shift accordingly.
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Creating a Name in the Stat List Editor
To create a name in the stat list editor, follow these steps.
2. Press [letter from A to Z or q] to enter the first letter of the name. The
first character cannot be a number.
3. Enter zero to four letters, q, or numbers to complete the new user-
created list name. List names can be one to five characters long.
4. Press Í or † to store the list name in the current column of the
stat list editor. The list name becomes an item on the LIST NAMES
menu (Chapter 11).
Removing a List from the Stat List Editor
To remove a list from the stat list editor, move the cursor onto the list
name and then press {. The list is not deleted from memory; it is only
removed from the stat list editor.
Note1: To delete a list name from memory, use the MEMORY MANAGEMENT/
DELETE secondary menu (Chapter 18).
Note 2: If you archive a list, it will be removed from the stat list editor.
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Removing All Lists and Restoring L1 through L6
You can remove all user-created lists from the stat list editor and restore
list names L1 through L6 to columns 1 through 6 in either of two ways.
• Reset all memory (Chapter 18).
Clearing All Elements from a List
You can clear all elements from a list in any of five ways.
• In the stat list editor, press } to move the cursor onto a list name,
and then press ‘ Í.
• In the stat list editor, move the cursor onto each element, and then
press { one by one.
• On the home screen or in the program editor, enter 0!dim(listname) to
set the dimension of listname to 0 (Chapter 11).
• Use ClrAllLists to clear all lists in memory (Chapter 18).
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Editing a List Element
To edit a list element, follow these steps.
1. Move the rectangular cursor onto the element you want to edit.
2. Press Í to move the cursor to the entry line.
Note: If you want to replace the current value, you can enter a new value
without first pressing Í. When you enter the first character, the current
value is cleared automatically.
3. Edit the element in the entry line.
• Press one or more keys to enter the new value. When you enter
the first character, the current value is cleared automatically.
• Press ~ to move the cursor to the character before which you want
to insert, press y 6, and then enter one or more characters.
• Press ~ to move the cursor to a character you want to delete, and
then press { to delete the character.
To cancel any editing and restore the original element at the
rectangular cursor, press ‘ Í.
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Note: You can enter expressions and variables for elements.
4. Press Í, }, or † to update the list. If you entered an expression,
it is evaluated. If you entered only a variable, the stored value is
displayed as a list element.
When you edit a list element in the stat list editor, the list is updated in
memory immediately.
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Attaching Formulas to List Names
Attaching a Formula to a List Name in Stat List Editor
You can attach a formula to a list name in the stat list editor, and then
display and edit the calculated list elements. When executed, the
attached formula must resolve to a list. Chapter 11 describes in detail the
concept of attaching formulas to list names.
To attach a formula to a list name that is stored in the stat list editor,
follow these steps.
1. Press … Í to display the stat list editor.
2. Press } to move the cursor to the top line.
3. Press | or ~, if necessary, to move the cursor onto the list name to
which you want to attach the formula.
Note: If a formula in quotation marks is displayed on the entry line, then a
formula is already attached to the list name. To edit the formula, press
Í, and then edit the formula.
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4. Press ƒ [ã], enter the formula, and press ƒ [ã].
Note: If you do not use quotation marks, the TI-83 Plus calculates and
displays the same initial list of answers, but does not attach the formula for
future calculations.
Note: Any user-created list name referenced in a formula must be preceded
by an Ù symbol (Chapter 11).
5. Press Í. The TI-83 Plus calculates each list element and stores it
to the list name to which the formula is attached. A lock symbol is
displayed in the stat list editor, next to the list name to which the
formula is attached.
lock symbol
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Using the Stat List Editor When Formula-Generated Lists Are
Displayed
When you edit an element of a list referenced in an attached formula, the
TI-83 Plus updates the corresponding element in the list to which the
formula is attached (Chapter 11).
When a list with a formula attached is displayed in the stat list editor and
you edit or enter elements of another displayed list, then the TI-83 Plus
takes slightly longer to accept each edit or entry than when no lists with
formulas attached are in view.
Tip: To speed editing time, scroll horizontally until no lists with formulas are
displayed, or rearrange the stat list editor so that no lists with formulas are
displayed.
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Handling Errors Resulting from Attached Formulas
On the home screen, you can attach to a list a formula that references
another list with dimension 0 (Chapter 11). However, you cannot display
the formula-generated list in the stat list editor or on the home screen
until you enter at least one element to the list that the formula
references.
All elements of a list referenced by an attached formula must be valid for
the attached formula. For example, if Real number mode is set and the
attached formula is log(L1), then each element of L1 must be greater than
0, since the logarithm of a negative number returns a complex result.
Tip: If an error menu is returned when you attempt to display a formula-
generated list in the stat list editor, you can select 2:Goto, write down the
formula that is attached to the list, and then press ‘ Í to detach (clear)
the formula. You then can use the stat list editor to find the source of the error.
After making the appropriate changes, you can reattach the formula to a list.
If you do not want to clear the formula, you can select 1:Quit, display the
referenced list on the home screen, and find and edit the source of the error. To
edit an element of a list on the home screen, store the new value to
listname(element#) (Chapter 11).
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Detaching Formulas from List Names
Detaching a Formula from a List Name
You can detach (clear) a formula from a list name in several ways.
For example:
• In the stat list editor, move the cursor onto the name of the list to
which a formula is attached. Press Í ‘ Í. All list
elements remain, but the formula is detached and the lock symbol
disappears.
• In the stat list editor, move the cursor onto an element of the list to
which a formula is attached. Press Í, edit the element, and then
press Í. The element changes, the formula is detached, and the
lock symbol disappears. All other list elements remain.
each formula is detached, and each lock symbol disappears. All list
names remain.
• Use ClrAllLists (Chapter 18). All elements of all lists in memory are
cleared, all formulas are detached from all list names, and all lock
symbols disappear. All list names remain.
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Editing an Element of a Formula-Generated List
As described above, one way to detach a formula from a list name is to
edit an element of the list to which the formula is attached. The
TI-83 Plus protects against inadvertently detaching the formula from the
list name by editing an element of the formula-generated list.
Because of the protection feature, you must press Í before you can
edit an element of a formula-generated list.
The protection feature does not allow you to delete an element of a list to
which a formula is attached. To delete an element of a list to which a
formula is attached, you must first detach the formula in any of the ways
described above.
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Switching Stat List Editor Contexts
Stat List Editor Contexts
The stat list editor has four contexts.
• View-elements context
• Edit-elements context
• View-names context
• Enter-name context
The stat list editor is first displayed in view-elements context. To switch
through the four contexts, select 1:Edit from the STAT EDIT menu and
follow these steps.
1. Press } to move the cursor onto a list name. You are
now in view-names context. Press ~ and | to view list
names stored in other stat list editor columns.
2. Press Í. You are now in edit-elements context.
You may edit any element in a list. All elements of the
current list are displayed in braces ( { } )in the entry
line. Press ~ and | to view more list elements.
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3. Press Í again. You are now in view-elements
context. Press ~, |, †, and } to view other list
elements. The current element’s full value is displayed
in the entry line.
4. Press Í again. You are now in edit-elements
context. You may edit the current element in the entry
line.
5. Press } until the cursor is on a list name, then press
y 6. You are now in enter-name context.
6. Press ‘. You are now in view-names context.
7. Press †. You are now back in view-elements context.
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Stat List Editor Contexts
View-Elements Context
In view-elements context, the entry line displays the list name, the
current element’s place in that list, and the full value of the current
element, up to 12 characters at a time. An ellipsis (...) indicates that the
element continues beyond 12 characters.
To page down the list six elements, press ƒ †. To page up six
elements, press ƒ }. To delete a list element, press {.
Remaining elements shift up one row. To insert a new element, press
y 6. 0 is the default value for a new element.
Edit-Elements Context
In edit-elements context, the data displayed in the entry line depends on
the previous context.
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• When you switch to edit-elements context from view-elements
context, the full value of the current element is displayed. You can
edit the value of this element, and then press † and } to edit other
list elements.
&
• When you switch to edit-elements context from view-names context,
the full values of all elements in the list are displayed. An ellipsis
indicates that list elements continue beyond the screen. You can
press ~ and | to edit any element in the list.
&
Note: In edit-elements context, you can attach a formula to a list name only if
you switched to it from view-names context.
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View-Names Context
In view-names context, the entry line displays the list name and the list
elements.
To remove a list from the stat list editor, press {. Remaining lists shift
to the left one column. The list is not deleted from memory.
To insert a name in the current column, press y 6. Remaining
columns shift to the right one column.
Enter-Name Context
In enter-name context, the Name= prompt is displayed in the entry line,
and alpha-lock is on.
At the Name= prompt, you can create a new list name, paste a list name
from L1 to L6 from the keyboard, or paste an existing list name from the
LIST NAMES menu (Chapter 11). The Ù symbol is not required at the Name=
prompt.
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To leave enter-name context without entering a list name, press ‘.
The stat list editor switches to view-names context.
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STAT EDIT Menu
STAT EDIT Menu
To display the STAT EDIT menu, press ….
EDIT CALC TESTS
1:Edit...
Displays the stat list editor.
2:SortA(
Sorts a list in ascending order.
Sorts a list in descending order.
Deletes all elements of a list.
Stores lists in the stat list editor.
3:SortD(
4:ClrList
5:SetUpEditor
Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items.
SortA(, SortD(
SortA( (sort ascending) sorts list elements from low to high values. SortD(
(sort descending) sorts list elements from high to low values. Complex
lists are sorted based on magnitude (modulus). SortA( and SortD( each
can sort in either of two ways.
• With one listname, SortA( and SortD( sort the elements in listname and
update the list in memory.
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• With two or more lists, SortA( and SortD( sort keylistname, and then sort
each dependlist by placing its elements in the same order as the
corresponding elements in keylistname. This lets you sort two-variable
data on X and keep the data pairs together. All lists must have the
same dimension.
The sorted lists are updated in memory.
SortA(listname)
SortD(listname)
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])
SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])
Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu.
ClrList
ClrList clears (deletes) from memory the elements of one or more
listnames. ClrList also detaches any formula attached to a listname.
ClrList listname1,listname2,...,listname n
Note: To clear from memory all elements of all list names, use ClrAllLists
(Chapter 18).
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SetUpEditor
With SetUpEditor you can set up the stat list editor to display one or more
listnames in the order that you specify. You can specify zero to 20
listnames.
Additionally, if you want to use listnames which happen to be archived, the
SetUp Editor will automatically unarchive the listnames and place them in
the stat list editor at the same time.
SetUpEditor [listname1,listname2,...,listname n]
SetUpEditor with one to 20 listnames removes all list names from the stat
list editor and then stores listnames in the stat list editor columns in the
specified order, beginning in column 1.
If you enter a listname that is not stored in memory already, then listname is
created and stored in memory; it becomes an item on the LIST NAMES
menu.
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Regression Model Features
Regression Model Features
STAT CALC menu items 3 through C are regression models. The automatic
residual list and automatic regression equation features apply to all
regression models. Diagnostics display mode applies to some regression
models.
Automatic Residual List
When you execute a regression model, the automatic residual list feature
computes and stores the residuals to the list name RESID. RESID
becomes an item on the LIST NAMES menu (Chapter 11).
The TI-83 Plus uses the formula below to compute RESID list elements.
The next section describes the variable RegEQ.
RESID = Ylistname N RegEQ(Xlistname)
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Automatic Regression Equation
Each regression model has an optional argument, regequ, for which you
can specify a Y= variable such as Y1. Upon execution, the regression
equation is stored automatically to the specified Y= variable and the Y=
function is selected.
Regardless of whether you specify a Y= variable for regequ, the
regression equation always is stored to the TI-83 Plus variable RegEQ,
which is item 1 on the VARS Statistics EQ secondary menu.
Note: For the regression equation, you can use the fixed-decimal mode setting
to control the number of digits stored after the decimal point (Chapter 1).
However, limiting the number of digits to a small number could affect the
accuracy of the fit.
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Diagnostics Display Mode
When you execute some regression models, the TI-83 Plus computes
2
and stores diagnostics values for r (correlation coefficient) and r
2
(coefficient of determination) or for R (coefficient of determination).
2
r and r are computed and stored for these regression models.
LinReg(ax+b)
LinReg(a+bx)
LnReg
ExpReg
PwrReg
2
R is computed and stored for these regression models.
QuadReg
CubicReg
QuartReg
2
The r and r that are computed for LnReg, ExpReg, and PwrReg are
based on the linearly transformed data. For example, for ExpReg
2
(y=ab^x), r and r are computed on ln y=ln a+x(ln b).
By default, these values are not displayed with the results of a
regression model when you execute it. However, you can set the
diagnostics display mode by executing the DiagnosticOn or DiagnosticOff
instruction. Each instruction is in the CATALOG (Chapter 15).
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Note: To set DiagnosticOn or DiagnosticOff from the home screen, press y
N, and then select the instruction for the mode you want. The instruction
is pasted to the home screen. Press Í to set the mode.
When DiagnosticOn is set, diagnostics are displayed with the results
when you execute a regression model.
When DiagnosticOff is set, diagnostics are not displayed with the results
when you execute a regression model.
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STAT CALC Menu
STAT CALC Menu
To display the STAT CALC menu, press … ~.
EDIT CALC TESTS
1:1-Var Stats
2:2-Var Stats
3:Med-Med
Calculates 1-variable statistics.
Calculates 2-variable statistics.
Calculates a median-median line.
Fits a linear model to data.
Fits a quadratic model to data.
Fits a cubic model to data.
4:LinReg(ax+b)
5:QuadReg
6:CubicReg
7:QuartReg
8:LinReg(a+bx)
9:LnReg
Fits a quartic model to data.
Fits a linear model to data.
Fits a logarithmic model to data.
Fits an exponential model to data.
Fits a power model to data.
Fits a logistic model to data.
Fits a sinusoidal model to data.
0:ExpReg
A:PwrReg
B:Logistic
C:SinReg
For each STAT CALC menu item, if neither Xlistname nor Ylistname is
specified, then the default list names are L1 and L2. If you do not specify
freqlist, then the default is 1 occurrence of each list element.
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Frequency of Occurrence for Data Points
For most STAT CALC menu items, you can specify a list of data
occurrences, or frequencies (freqlist).
Each element in freqlist indicates how many times the corresponding data
point or data pair occurs in the data set you are analyzing.
For example, if L1={15,12,9,14} and ÙFREQ={1,4,1,3}, then the TI-83 Plus
interprets the instruction 1.Var Stats L1, ÙFREQ to mean that 15 occurs
once, 12 occurs four times, 9 occurs once, and 14 occurs three times.
Each element in freqlist must be ‚ 0, and at least one element must be > 0.
Noninteger freqlist elements are valid. This is useful when entering
frequencies expressed as percentages or parts that add up to 1.
However, if freqlist contains noninteger frequencies, Sx and Sy are
undefined; values are not displayed for Sx and Sy in the statistical
results.
1.Var Stats
1.Var Stats (one-variable statistics) analyzes data with one measured
variable. Each element in freqlist is the frequency of occurrence for each
corresponding data point in Xlistname. freqlist elements must be real
numbers > 0.
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1.Var Stats [Xlistname,freqlist]
2.Var Stats
2.Var Stats (two-variable statistics) analyzes paired data. Xlistname is the
independent variable. Ylistname is the dependent variable. Each element
in freqlist is the frequency of occurrence for each data pair
(Xlistname,Ylistname).
2.Var Stats [Xlistname,Ylistname,freqlist]
Med.Med (ax+b)
Med.Med (median-median) fits the model equation y=ax+b to the data
using the median-median line (resistant line) technique, calculating the
summary points x1, y1, x2, y2, x3, and y3. Med.Med displays values for
a (slope) and b (y-intercept).
Med.Med [Xlistname,Ylistname,freqlist,regequ]
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LinReg (ax+b)
LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data
using a least-squares fit. It displays values for a (slope) and b (y-intercept);
2
when DiagnosticOn is set, it also displays values for r and r.
LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]
QuadReg (ax2+bx+c)
QuadReg (quadratic regression) fits the second-degree polynomial
y=ax2+bx+c to the data. It displays values for a, b, and c; when
2
DiagnosticOn is set, it also displays a value for R . For three data points,
the equation is a polynomial fit; for four or more, it is a polynomial
regression. At least three data points are required.
QuadReg [Xlistname,Ylistname,freqlist,regequ]
CubicReg—(ax3+bx2+cx+d)
CubicReg (cubic regression) fits the third-degree polynomial
y=ax3+bx2+cx+d to the data. It displays values for a, b, c, and d; when
2
DiagnosticOn is set, it also displays a value for R . For four points, the
equation is a polynomial fit; for five or more, it is a polynomial regression.
At least four points are required.
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CubicReg [Xlistname,Ylistname,freqlist,regequ]
QuartReg—(ax4+bx3+cx2+ dx+e)
QuartReg (quartic regression) fits the fourth-degree polynomial
y=ax4+bx3+cx2+dx+e to the data. It displays values for a, b, c, d, and e;
2
when DiagnosticOn is set, it also displays a value for R . For five points,
the equation is a polynomial fit; for six or more, it is a polynomial
regression. At least five points are required.
QuartReg [Xlistname,Ylistname,freqlist,regequ]
LinReg—(a+bx)
LinReg(a+bx) (linear regression) fits the model equation y=a+bx to the data
using a least-squares fit. It displays values for a (y-intercept) and b (slope);
2
when DiagnosticOn is set, it also displays values for r and r.
LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ]
LnReg—(a+b ln(x))
LnReg (logarithmic regression) fits the model equation y=a+b ln(x) to the
data using a least-squares fit and transformed values ln(x) and y. It
displays values for a and b; when DiagnosticOn is set, it also displays
2
values for r and r.
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LnReg [Xlistname,Ylistname,freqlist,regequ]
ExpReg—(abx)
ExpReg (exponential regression) fits the model equation y=abx to the data
using a least-squares fit and transformed values x and ln(y). It displays
values for a and b; when DiagnosticOn is set, it also displays values for r
2
and r.
ExpReg [Xlistname,Ylistname,freqlist,regequ]
PwrReg—(axb)
PwrReg (power regression) fits the model equation y=axb to the data using
a least-squares fit and transformed values ln(x) and ln(y). It displays
values for a and b; when DiagnosticOn is set, it also displays values for r
2
and r.
PwrReg [Xlistname,Ylistname,freqlist,regequ]
Logistic—c/(1+aäeLbx)
Logistic fits the model equation y=c/(1+aäeLbx) to the data using an
iterative least-squares fit. It displays values for a, b, and c.
Logistic [Xlistname,Ylistname,freqlist,regequ]
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SinReg—a sin(bx+c)+d
SinReg (sinusoidal regression) fits the model equation y=a sin(bx+c)+d to
the data using an iterative least-squares fit. It displays values for a, b, c,
and d. At least four data points are required. At least two data points per
cycle are required in order to avoid aliased frequency estimates.
SinReg [iterations,Xlistname,Ylistname,period,regequ]
iterations is the maximum number of times the algorithm will iterate to find
a solution. The value for iterations can be an integer ‚ 1 and 16; if not
specified, the default is 3. The algorithm may find a solution before
iterations is reached. Typically, larger values for iterations result in longer
execution times and better accuracy for SinReg, and vice versa.
A period guess is optional. If you do not specify period, the difference
between time values in Xlistname must be equal and the time values must
be ordered in ascending sequential order. If you specify period, the
algorithm may find a solution more quickly, or it may find a solution when
it would not have found one if you had omitted a value for period. If you
specify period, the differences between time values in Xlistname can be
unequal.
Note: The output of SinReg is always in radians, regardless of the Radian/Degree
mode setting.
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SinReg Example: Daylight Hours in Alaska for One Year
Compute the regression model for the number of hours of daylight in
Alaska during one year.
&
&
1 period
With noisy data, you will achieve better convergence results when you
specify an accurate estimate for period. You can obtain a period guess in
either of two ways.
• Plot the data and trace to determine the x-distance between the
beginning and end of one complete period, or cycle. The illustration
above and to the right graphically depicts a complete period, or cycle.
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• Plot the data and trace to determine the x-distance between the
beginning and end of N complete periods, or cycles. Then divide the
total distance by N.
After your first attempt to use SinReg and the default value for iterations to
fit the data, you may find the fit to be approximately correct, but not
optimal. For an optimal fit, execute SinReg 16,Xlistname,Ylistname,2p / b
where b is the value obtained from the previous SinReg execution.
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Statistical Variables
The statistical variables are calculated and stored as indicated below. To
access these variables for use in expressions, press , and select
5:Statistics. Then select the VARS menu shown in the column below under
VARS menu. If you edit a list or change the type of analysis, all statistical
variables are cleared.
1
.
Var
2
.
Var
VARS
menu
Variables
Stats
Stats
Other
mean of x values
v
v
XY
G
sum of x values
sum of x2 values
Gx
Gx2
Sx
sx
n
Gx
Gx2
Sx
sx
G
sample standard deviation of x
population standard deviation of x
number of data points
mean of y values
XY
XY
XY
XY
G
n
w
sum of y values
Gy
sum of y2 values
Gy2
Sy
sy
G
sample standard deviation of y
population standard deviation of y
sum of x … y
XY
XY
G
Gxy
minX
minimum of x values
minX
XY
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1
.
Var
2
.
Var
VARS
menu
Variables
Stats
Stats
maxX
minY
maxY
Other
maximum of x values
minimum of y values
maximum of y values
1st quartile
maxX
XY
XY
XY
Q1
Med
Q3
PTS
PTS
PTS
EQ
median
3rd quartile
regression/fit coefficients
a, b
polynomial, Logistic, and SinReg
a, b, c,
EQ
coefficients
d, e
correlation coefficient
r
EQ
EQ
coefficient of determination
regression equation
r2, R2
RegEQ
EQ
summary points (Med.Med only)
x1, y1, x2,
PTS
y2, x3, y3
Q1 and Q3
The first quartile (Q1) is the median of points between minX and Med
(median). The third quartile (Q3) is the median of points between Med
and maxX.
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Statistical Analysis in a Program
Entering Stat Data
You can enter statistical data, calculate statistical results, and fit models
to data from a program. You can enter statistical data into lists directly
within the program (Chapter 11).
Statistical Calculations
To perform a statistical calculation from a program, follow these steps.
1. On a blank line in the program editor, select the type of calculation
from the STAT CALC menu.
2. Enter the names of the lists to use in the calculation. Separate the list
names with a comma.
3. Enter a comma and then the name of a Y= variable, if you want to store
the regression equation to a Y= variable.
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Statistical Plotting
Steps for Plotting Statistical Data in Lists
You can plot statistical data that is stored in lists. The six types of plots
available are scatter plot, xyLine, histogram, modified box plot, regular
box plot, and normal probability plot. You can define up to three plots.
To plot statistical data in lists, follow these steps.
1. Store the stat data in one or more lists.
2. Select or deselect Y= functions as appropriate.
3. Define the stat plot.
4. Turn on the plots you want to display.
5. Define the viewing window.
6. Display and explore the graph.
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" (Scatter)
Scatter plots plot the data points from Xlist and Ylist as coordinate pairs,
showing each point as a box ( › ), cross ( + ), or dot ( ¦ ). Xlist and Ylist
must be the same length. You can use the same list for Xlist and Ylist.
Ó (xyLine)
xyLine is a scatter plot in which the data points are plotted and
connected in order of appearance in Xlist and Ylist. You may want to use
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Ò (Histogram)
Histogram plots one-variable data. The Xscl window variable value
determines the width of each bar, beginning at Xmin. ZoomStat adjusts
Xmin, Xmax, Ymin, and Ymax to include all values, and also adjusts Xscl.
The inequality (Xmax N Xmin) à Xscl 47 must be true. A value that occurs
on the edge of a bar is counted in the bar to the right.
Õ (ModBoxplot)
ModBoxplot (modified box plot) plots one-variable data, like the regular
box plot, except points that are 1.5 ä Interquartile Range beyond the
quartiles. (The Interquartile Range is defined as the difference between
the third quartile Q3 and the first quartile Q1.) These points are plotted
individually beyond the whisker, using the Mark (› or + or ¦) you select.
You can trace these points, which are called outliers.
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The prompt for outlier points is x=, except when the outlier is the
maximum point (maxX) or the minimum point (minX). When outliers exist,
the end of each whisker will display x=. When no outliers exist, minX and
maxX are the prompts for the end of each whisker. Q1, Med (median), and
Q3 define the box.
Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and
Ymax. When two box plots are plotted, the first one plots at the top of the
screen and the second plots in the middle. When three are plotted, the
first one plots at the top, the second in the middle, and the third at the
bottom.
Ö (Boxplot)
Boxplot (regular box plot) plots one-variable data. The whiskers on the
plot extend from the minimum data point in the set (minX) to the first
quartile (Q1) and from the third quartile (Q3) to the maximum point
(maxX). The box is defined by Q1, Med (median), and Q3.
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Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and
Ymax. When two box plots are plotted, the first one plots at the top of the
screen and the second plots in the middle. When three are plotted, the
first one plots at the top, the second in the middle, and the third at the
bottom.
Ô (NormProbPlot)
NormProbPlot (normal probability plot) plots each observation X in
Data List versus the corresponding quantile z of the standard normal
distribution. If the plotted points lie close to a straight line, then the plot
indicates that the data are normal.
Enter a valid list name in the Data List field. Select X or Y for the Data Axis
setting.
• If you select X, the TI-83 Plus plots the data on the x-axis and the
z-values on the y-axis.
• If you select Y, the TI-83 Plus plots the data on the y-axis and the
z-values on the x-axis.
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3. Press Í to select On if you want to plot the statistical data
immediately. The definition is stored whether you select On or Off.
4. Select the type of plot. Each type prompts for the options checked in
this table.
Plot Type
Data List Data Axis
XList
YList
Mark
Freq
œ
" Scatter
Ó
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Ò
œ
œ
Õ
œ
Ö
œ
œ
Ô
œ
œ
œ
5. Enter list names or select options for the plot type.
•
•
•
Xlist (list name containing independent data)
Ylist (list name containing dependent data)
Mark (› or + or ¦)
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•
•
•
Freq (frequency list for Xlist elements; default is 1)
Data List (list name for NormProbPlot)
Data Axis (axis on which to plot Data List)
Displaying Other Stat Plot Editors
Each stat plot has a unique stat plot editor. The name of the current stat
plot (Plot1, Plot2, or Plot3) is highlighted in the top line of the stat plot
editor. To display the stat plot editor for a different plot, press }, ~, and
| to move the cursor onto the name in the top line, and then press
Í. The stat plot editor for the selected plot is displayed, and the
selected name remains highlighted.
Turning On and Turning Off Stat Plots
PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the
home screen or a program. With no plot number, PlotsOn turns on all
plots and PlotsOff turns off all plots. With one or more plot numbers (1, 2,
and 3), PlotsOn turns on specified plots, and PlotsOff turns off specified
plots.
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PlotsOff [1,2,3]
PlotsOn [1,2,3]
Note: You also can turn on and turn off stat plots in the top line of the Y= editor
(Chapter 3).
Defining the Viewing Window
Stat plots are displayed on the current graph. To define the viewing
window, press p and enter values for the window variables.
ZoomStat redefines the viewing window to display all statistical data
points.
Tracing a Stat Plot
When you trace a scatter plot or xyLine, tracing begins at the first
element in the lists.
When you trace a histogram, the cursor moves from the top center of
one column to the top center of the next, starting at the first column.
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When you trace a box plot, tracing begins at Med (the median). Press |
to trace to Q1 and minX. Press ~ to trace to Q3 and maxX.
When you press } or † to move to another plot or to another Y=
function, tracing moves to the current or beginning point on that plot (not
the nearest pixel).
The ExprOn/ExprOff format setting applies to stat plots (Chapter 3). When
ExprOn is selected, the plot number and plotted data lists are displayed
in the top-left corner.
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Statistical Plotting in a Program
Defining a Stat Plot in a Program
To display a stat plot from a program, define the plot, and then display
the graph.
To define a stat plot from a program, begin on a blank line in the
program editor and enter data into one or more lists; then, follow these
steps.
1. Press y , to display the STAT PLOTS menu.
2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the
cursor location.
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3. Press y , ~ to display the STAT TYPE menu.
4. Select the type of plot, which pastes the name of the plot type to the
cursor location.
5. Press ¢. Enter the list names, separated by commas.
6. Press ¢ y , | to display the STAT PLOT MARK menu. (This
step is not necessary if you selected 3:Histogram or 5:Boxplot in
step 4.)
Select the type of mark (› or + or ¦) for each data point. The selected
mark symbol is pasted to the cursor location.
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Chapter 13:
Inferential Statistics and Distributions
Getting Started: Mean Height of a
Population
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to estimate the mean height of a population of women given
the random sample below. Because heights among a biological population tend
to be normally distributed, a t distribution confidence interval can be used when
estimating the mean. The 10 height values below are the first 10 of 90 values,
randomly generated from a normally distributed population with an assumed
mean of 165.1 centimeters and a standard deviation of 6.35 centimeters
(randNorm(165.1,6.35,90) with a seed of 789).
Height (in centimeters) of Each of 10 Women
169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04
167.15 159.53
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1. Press … Í to display the stat list editor.
Press } to move the cursor onto L1, and then
press y 6. The Name= prompt is displayed
on the bottom line. The Ø cursor indicates that
alpha-lock is on. The existing list name columns
shift to the right.
Note: Your stat editor may not look like the one
pictured here, depending on the lists you have
already stored.
2. Enter [H] [G] [H] [T] at the Name= prompt, and
then press Í. The list to which you will
store the women’s height data is created.
Press † to move the cursor onto the first row of
the list. HGHT(1)= is displayed on the bottom line.
3. Press 169 Ë 43 to enter the first height value.
As you enter it, it is displayed on the bottom
line.
Press Í. The value is displayed in the first
row, and the rectangular cursor moves to the
next row.
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Enter the other nine height values the same
way.
4. Press … | to display the STAT TESTS menu,
and then press † until 8:TInterval is highlighted.
5. Press Í to select 8:TInterval. The inferential
stat editor for TInterval is displayed. If Data is not
selected for Inpt:, press | Í to select Data.
Press † and [H] [G] [H] [T] at the List: prompt
(alpha-lock is on).
Press † † Ë 99 to enter a 99 percent
confidence level at the C.Level: prompt.
6. Press † to move the cursor onto Calculate, and
then press Í. The confidence interval is
calculated, and the TInterval results are
displayed on the home screen.
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Interpret the results.
The first line, (159.74,173.94), shows that the 99 percent confidence
interval for the population mean is between about 159.74 centimeters
and 173.94 centimeters. This is about a 14.2 centimeters spread.
The .99 confidence level indicates that in a very large number of
samples, we expect 99 percent of the intervals calculated to contain the
population mean. The actual mean of the population sampled is 165.1
centimeters, which is in the calculated interval.
The second line gives the mean height of the sample þ used to compute
this interval. The third line gives the sample standard deviation Sx. The
bottom line gives the sample size n.
To obtain a more precise bound on the population mean m of women’s
heights, increase the sample size to 90. Use a sample mean þ of 163.8
and sample standard deviation Sx of 7.1 calculated from the larger
random sample. This time, use the Stats (summary statistics) input
option.
7. Press … | 8 to display the inferential stat
editor for TInterval.
Press ~ Í to select Inpt:Stats. The editor
changes so that you can enter summary
statistics as input.
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8. Press † 163 Ë 8 Í to store 163.8 to ü.
Press 7 Ë 1 Í to store 7.1 to Sx.
Press 90 Í to store 90 to n.
9. Press † to move the cursor onto Calculate, and
then press Í to calculate the new 99
percent confidence interval. The results are
displayed on the home screen.
If the height distribution among a population of women is normally
distributed with a mean m of 165.1 centimeters and a standard deviation
σ of 6.35 centimeters, what height is exceeded by only 5 percent of the
women (the 95th percentile)?
10.Press ‘ to clear the home screen.
Press y = to display the DISTR
(distributions) menu.
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11. Press 3 to paste invNorm( to the home screen.
Press Ë 95 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤ Í.
.95 is the area, 165.1 is µ, and 6.35 is σ.
The result is displayed on the home screen; it shows that five percent of
the women are taller than 175.5 centimeters.
Now graph and shade the top 5 percent of the population.
12. Press p and set the window variables to
these values.
Xmin=145
Xmax=185
Xscl=5
Ymin=L.02
Ymax=.08
Yscl=0
Xres=1
13. Press y = ~ to display the DISTR DRAW
menu.
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14. Press Í to paste ShadeNorm( to the home
screen.
Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6
Ë 35 ¤.
Ans (175.5448205 from step 11) is the lower
bound. 1å99 is the upper bound. The normal
curve is defined by a mean µ of 165.1 and a
standard deviation σ of 6.35.
15. Press Í to plot and shade the normal
curve.
Area is the area above the 95th percentile. low
is the lower bound. up is the upper bound.
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Inferential Stat Editors
Displaying the Inferential Stat Editors
When you select a hypothesis test or confidence interval instruction from
the home screen, the appropriate inferential statistics editor is displayed.
The editors vary according to each test or interval’s input requirements.
Below is the inferential stat editor for T-Test.
Note: When you select the ANOVA( instruction, it is pasted to the home screen.
ANOVA( does not have an editor screen.
Using an Inferential Stat Editor
To use an inferential stat editor, follow these steps.
1. Select a hypothesis test or confidence interval from the STAT TESTS
menu. The appropriate editor is displayed.
2. Select Data or Stats input, if the selection is available. The appropriate
editor is displayed.
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3. Enter real numbers, list names, or expressions for each argument in
the editor.
4. Select the alternative hypothesis (ƒ, <, or >) against which to test, if
the selection is available.
5. Select No or Yes for the Pooled option, if the selection is available.
6. Select Calculate or Draw (when Draw is available) to execute the
instruction.
• When you select Calculate, the results are displayed on the home
screen.
• When you select Draw, the results are displayed in a graph.
This chapter describes the selections in the above steps for each
hypothesis test and confidence interval instruction.
Select Data or
Stats input
Select an
alternative
hypothesis
Enter values
for arguments
Select
Calculate or
Draw output
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Selecting Data or Stats
Most inferential stat editors prompt you to select one of two types of
2
input. (1.PropZInt and 2.PropZTest, 1.PropZInt and 2.PropZInt, c .Test, and
LinRegTTest do not.)
• Select Data to enter the data lists as input.
• Select Stats to enter summary statistics, such as þ, Sx, and n, as
input.
To select Data or Stats, move the cursor to either Data or Stats, and then
press Í.
Entering the Values for Arguments
Inferential stat editors require a value for every argument. If you do not
When you enter values in any inferential stat editor, the TI-83 Plus stores
them in memory so that you can run many tests or intervals without
having to reenter every value.
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Selecting an Alternative Hypothesis (ƒ < >)
Most of the inferential stat editors for the hypothesis tests prompt you to
select one of three alternative hypotheses.
• The first is a ƒ alternative hypothesis, such as mƒm0 for the Z.Test.
• The second is a < alternative hypothesis, such as m1<m2 for the
2.SampTTest.
• The third is a > alternative hypothesis, such as p1>p2 for the
2.PropZTest.
To select an alternative hypothesis, move the cursor to the appropriate
alternative, and then press Í.
Selecting the Pooled Option
Pooled (2.SampTTest and 2.SampTInt only) specifies whether the
variances are to be pooled for the calculation.
• Select No if you do not want the variances pooled. Population
variances can be unequal.
• Select Yes if you want the variances pooled. Population variances are
assumed to be equal.
To select the Pooled option, move the cursor to Yes, and then press
Í.
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Selecting Calculate or Draw for a Hypothesis Test
After you have entered all arguments in an inferential stat editor for a
hypothesis test, you must select whether you want to see the calculated
results on the home screen (Calculate) or on the graph screen (Draw).
•
•
Calculate calculates the test results and displays the outputs on the
home screen.
Draw draws a graph of the test results and displays the test statistic
and p-value with the graph. The window variables are adjusted
automatically to fit the graph.
To select Calculate or Draw, move the cursor to either Calculate or Draw,
and then press Í. The instruction is immediately executed.
Selecting Calculate for a Confidence Interval
After you have entered all arguments in an inferential stat editor for a
confidence interval, select Calculate to display the results. The Draw
option is not available.
When you press Í, Calculate calculates the confidence interval
results and displays the outputs on the home screen.
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Bypassing the Inferential Stat Editors
To paste a hypothesis test or confidence interval instruction to the home
screen without displaying the corresponding inferential stat editor, select
the instruction you want from the CATALOG menu. Appendix A describes
the input syntax for each hypothesis test and confidence interval
instruction.
Note: You can paste a hypothesis test or confidence interval instruction to a
command line in a program. From within the program editor, select the
instruction from either the CATALOG (Chapter 15) or the STAT TESTS menu.
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STAT TESTS Menu
STAT TESTS Menu
To display the STAT TESTS menu, press … |. When you select an
inferential statistics instruction, the appropriate inferential stat editor is
displayed.
Most STAT TESTS instructions store some output variables to memory. For
a list of these variables, see the Test and Interval Output Variables table.
EDIT CALC TESTS
1: Z-Test...
Test for 1 m, known s
2: T-Test...
Test for 1 m, unknown s
3: 2-SampZTest...
4: 2-SampTTest...
5: 1-PropZTest...
6: 2-PropZTest...
7: ZInterval...
8: TInterval...
9: 2-SampZInt...
0: 2-SampTInt...
A: 1-PropZInt...
B: 2-PropZInt...
C: c2-Test...
Test comparing 2 m’s, known s’s
Test comparing 2 m’s, unknown s’s
Test for 1 proportion
Test comparing 2 proportions
Confidence interval for 1 m, known s
Confidence interval for 1 m, unknown s
Confidence interval for difference of 2 m’s, known s’s
Confidence interval for difference of 2 m’s, unknown s’s
Confidence interval for 1 proportion
Confidence interval for difference of 2 proportions
Chi-square test for 2-way tables
Test comparing 2 s’s
D: 2-SampÛTest...
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EDIT CALC TESTS
E: LinRegTTest...
t test for regression slope and r
F: ANOVA(
One-way analysis of variance
Note: When a new test or interval is computed, all previous output variables are
invalidated.
Inferential Stat Editors for the STAT TESTS Instructions
In this chapter, the description of each STAT TESTS instruction shows the
unique inferential stat editor for that instruction with example arguments.
• Descriptions of instructions that offer the Data/Stats input choice show
both types of input screens.
• Descriptions of instructions that do not offer the Data/Stats input
choice show only one input screen.
The description then shows the unique output screen for that instruction
with the example results.
• Descriptions of instructions that offer the Calculate/Draw output choice
show both types of screens: calculated and graphic results.
• Descriptions of instructions that offer only the Calculate output choice
show the calculated results on the home screen.
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Z.Test
Z.Test (one-sample z test; item 1) performs a hypothesis test for a single
unknown population mean m when the population standard deviation s is
known. It tests the null hypothesis H0: m=m0 against one of the
alternatives below.
• Ha: mƒm0 (m:ƒm0)
• Ha: m<m0 (m:<m0)
• Ha: m>m0 (m:>m0)
In the example:
L1={299.4 297.7 301 298.9 300.2 297}
Data
Stats
Input:
,
,
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Data
Stats
Calculated results:
,
,
Drawn results:
Note: All STAT TESTS examples assume a fixed-decimal mode setting of 4
(Chapter 1). If you set the decimal mode to Float or a different fixed-decimal
setting, your output may differ from the output in the examples.
T.Test
T.Test (one-sample t test; item 2) performs a hypothesis test for a single
unknown population mean m when the population standard deviation s is
unknown. It tests the null hypothesis H0: m=m0 against one of the
alternatives below.
• Ha: mƒm0 (m:ƒm0)
• Ha: m<m0 (m:<m0)
• Ha: m>m0 (m:>m0)
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In the example:
TEST={91.9 97.8 111.4 122.3 105.4 95}
Data
Stats
Input:
,
,
Calculated results:
,
,
Drawn results:
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2.SampZTest
2.SampZTest (two-sample z test; item 3) tests the equality of the means of
two populations (m1 and m2) based on independent samples when both
population standard deviations (s1 and s2) are known. The null
hypothesis H0: m1=m2 is tested against one of the alternatives below.
• Ha: m1ƒm2 (m1:ƒm2)
• Ha: m1<m2 (m1:<m2)
• Ha: m1>m2 (m1:>m2)
In the example:
LISTA={154 109 137 115 140}
LISTB={108 115 126 92 146}
Data
Stats
Input:
,
,
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Calculated results:
,
,
Drawn results:
2.SampTTest
2.SampTTest (two-sample t test; item 4) tests the equality of the means of
two populations (m1 and m2) based on independent samples when
neither population standard deviation (s1 or s2) is known. The null
hypothesis H0: m1=m2 is tested against one of the alternatives below.
• Ha: m1ƒm2 (m1:ƒm2)
• Ha: m1<m2 (m1:<m2)
• Ha: m1>m2 (m1:>m2)
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In the example:
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
Data
Stats
Input:
,
,
Calculated results:
,
,
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Drawn results:
1.PropZTest
1.PropZTest (one-proportion z test; item 5) computes a test for an
unknown proportion of successes (prop). It takes as input the count of
successes in the sample x and the count of observations in the sample n.
1.PropZTest tests the null hypothesis H0: prop=p0 against one of the
alternatives below.
• Ha: propƒp0 (prop:ƒp0)
• Ha: prop<p0 (prop:<p0)
• Ha: prop>p0 (prop:>p0)
Input:
,
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Calculated results:
,
Drawn results:
2.PropZTest
2.PropZTest (two-proportion z test; item 6) computes a test to compare
the proportion of successes (p1 and p2) from two populations. It takes as
input the count of successes in each sample (x and x ) and the count of
1
2
observations in each sample (n and n ). 2.PropZTest tests the null
1
2
hypothesis H0: p1=p2 (using the pooled sample proportion Ç) against
one of the alternatives below.
• Ha: p1ƒp2 (p1:ƒp2)
• Ha: p1<p2 (p1:<p2)
• Ha: p1>p2 (p1:>p2)
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Input:
,
,
Calculated results:
Drawn results:
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ZInterval
ZInterval (one-sample z confidence interval; item 7) computes a
confidence interval for an unknown population mean m when the
population standard deviation s is known. The computed confidence
interval depends on the user-specified confidence level.
In the example:
L1={299.4 297.7 301 298.9 300.2 297}
Data
Stats
Input:
,
,
Calculated results:
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TInterval
TInterval (one-sample t confidence interval; item 8) computes a
confidence interval for an unknown population mean m when the
population standard deviation s is unknown. The computed confidence
interval depends on the user-specified confidence level.
In the example:
L6={1.6 1.7 1.8 1.9}
Data
Stats
Input:
,
,
Calculated results:
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2.SampZInt
2.SampZInt (two-sample z confidence interval; item 9) computes a
confidence interval for the difference between two population means
(m1Nm2) when both population standard deviations (s1 and s2) are
known. The computed confidence interval depends on the user-specified
confidence level.
In the example:
LISTC={154 109 137 115 140}
LISTD={108 115 126 92 146}
Data
Stats
Input:
,
,
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Calculated results:
2.SampTInt
2.SampTInt (two-sample t confidence interval; item 0) computes a
confidence interval for the difference between two population means
(m1Nm2) when both population standard deviations (s1 and s2) are
unknown. The computed confidence interval depends on the user-
specified confidence level.
In the example:
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
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Data
Stats
Input:
,
,
Calculated results:
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1.PropZInt
1.PropZInt (one-proportion z confidence interval; item A) computes a
confidence interval for an unknown proportion of successes. It takes as
input the count of successes in the sample x and the count of
observations in the sample n. The computed confidence interval depends
on the user-specified confidence level.
Input:
,
Calculated results:
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2.PropZInt
2.PropZInt (two-proportion z confidence interval; item B) computes a
confidence interval for the difference between the proportion of
successes in two populations (p1Np2). It takes as input the count of
successes in each sample (x and x ) and the count of observations in
1
2
each sample (n and n ). The computed confidence interval depends on
1
2
the user-specified confidence level.
Input:
,
Calculated results:
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c2.Test
c2.Test (chi-square test; item C) computes a chi-square test for
association on the two-way table of counts in the specified Observed
matrix. The null hypothesis H0 for a two-way table is: no association
exists between row variables and column variables. The alternative
hypothesis is: the variables are related.
Before computing a c2.Test, enter the observed counts in a matrix. Enter
that matrix variable name at the Observed: prompt in the c2.Test editor;
default=[A]. At the Expected: prompt, enter the matrix variable name to
which you want the computed expected counts to be stored; default=[B].
Note: Press y Ž
~ ~ 1 to select 1:[A]
from the MATRX EDIT
menu.
Matrix editor:
Input:
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Inferential Statistics and Distributions
412
,
,
Note: Press y Ž
[B] Í to display
matrix [B].
Calculated results:
Drawn results:
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Inferential Statistics and Distributions
413
2.SampÜTest
2.SampÜTest (two-sample Û-test; item D) computes an Û-test to compare
two normal population standard deviations (s1 and s2). The population
means and standard deviations are all unknown. 2.SampÜTest, which
uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis
H0: s1=s2 against one of the alternatives below.
• Ha: s1ƒs2 (s1:ƒs2)
• Ha: s1<s2 (s1:<s2)
• Ha: s1>s2 (s1:>s2)
In the example:
SAMP4={
SAMP5={
7 L4 18 17 L3 L5 1 10 11L2}
L1 12 L1 L3 3 L5 5 2L11L1L3}
Data
Stats
Input:
,
,
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414
Calculated results:
,
,
Drawn results:
LinRegTTest
LinRegTTest (linear regression t test; item E) computes a linear
regression on the given data and a t test on the value of slope b and the
correlation coefficient r for the equation y=a+bx. It tests the null
hypothesis H0: b=0 (equivalently, r=0) against one of the alternatives
below.
• Ha: bƒ0 and rƒ0 (b & r:ƒ0)
• Ha: b<0 and r<0 (b & r:<0)
• Ha: b>0 and r>0 (b & r:>0)
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The regression equation is automatically stored to RegEQ (VARS Statistics
EQ secondary menu). If you enter a Y= variable name at the RegEQ:
prompt, the calculated regression equation is automatically stored to the
specified Y= equation. In the example below, the regression equation is
stored to Y1, which is then selected (turned on).
In the example:
L3={
L4={
38 56 59 6474}
41 63 70 7284}
Input:
,
Calculated results:
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When LinRegTTest is executed, the list of residuals is created and stored
to the list name RESID automatically. RESID is placed on the LIST NAMES
menu.
Note: For the regression equation, you can use the fix-decimal mode setting to
control the number of digits stored after the decimal point (Chapter 1).
However, limiting the number of digits to a small number could affect the
accuracy of the fit.
ANOVA(
ANOVA( (one-way analysis of variance; item F) computes a one-way
analysis of variance for comparing the means of two to 20 populations.
The ANOVA procedure for comparing these means involves analysis of
the variation in the sample data. The null hypothesis H0: m1=m2=...=mk is
tested against the alternative Ha: not all m1...mk are equal.
ANOVA(list1,list2[,...,list20])
In the example:
L1={7 4 6 6 5}
L2={6 5 5 8 7}
L3={4 7 6 7 6}
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Input:
,
Calculated results:
Note: SS is sum of squares and MS is mean square.
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418
Inferential Statistics Input Descriptions
The tables in this section describe the inferential statistics inputs
discussed in this chapter. You enter values for these inputs in the
inferential stat editors. The tables present the inputs in the same order
that they appear in this chapter.
Input
Description
m
Hypothesized value of the population mean that you are
testing.
0
s
The known population standard deviation; must be a real
number > 0.
List
The name of the list containing the data you are testing.
Freq
The name of the list containing the frequency values for
the data in List. Default=1. All elements must be integers
| 0.
Calculate/Draw
Determines the type of output to generate for tests and
intervals. Calculate displays the output on the home
screen. In tests, Draw draws a graph of the results.
v, Sx, n
Summary statistics (mean, standard deviation, and
sample size) for the one-sample tests and intervals.
s1
The known population standard deviation from the first
population for the two-sample tests and intervals. Must
be a real number > 0.
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419
Input
Description
s2
The known population standard deviation from the
second population for the two-sample tests and intervals.
Must be a real number > 0.
List1, List2
The names of the lists containing the data you are testing
for the two-sample tests and intervals. Defaults are L1
and L2, respectively.
Freq1, Freq2
The names of the lists containing the frequencies for the
data in List1 and List2 for the two-sample tests and
intervals. Defaults=1. All elements must be integers | 0.
v1, Sx1, n1, v2, Sx2, Summary statistics (mean, standard deviation, and
n2
sample size) for sample one and sample two in the two-
sample tests and intervals.
Pooled
Specifies whether variances are to be pooled for
2.SampTTest and 2.SampTInt. No instructs the TI.83 not to
pool the variances. Yes instructs the TI.83 to pool the
variances.
p0
x
The expected sample proportion for 1.PropZTest. Must be
a real number, such that 0 < p0 < 1.
The count of successes in the sample for the 1.PropZTest
and 1.PropZInt. Must be an integer ‚ 0.
n
The count of observations in the sample for the
1.PropZTest and 1.PropZInt. Must be an integer > 0.
x1
The count of successes from sample one for the
2.PropZTest and 2.PropZInt. Must be an integer ‚ 0.
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Input
Description
x2
The count of successes from sample two for the
2.PropZTest and 2.PropZInt. Must be an integer ‚ 0.
n1
The count of observations in sample one for the
2.PropZTest and 2.PropZInt. Must be an integer > 0.
n2
The count of observations in sample two for the
2.PropZTest and 2.PropZInt. Must be an integer > 0.
C.Level
The confidence level for the interval instructions. Must be
‚ 0 and <100. If it is ‚ 1, it is assumed to be given as a
percent and is divided by 100. Default=0.95.
Observed (Matrix)
The matrix name that represents the columns and rows
for the observed values of a two-way table of counts for
the c .Test. Observed must contain all integers ‚ 0. Matrix
2
dimensions must be at least 2×2.
Expected (Matrix)
Xlist, Ylist
The matrix name that specifies where the expected
values should be stored. Expected is created upon
2
successful completion of the c .Test.
The names of the lists containing the data for LinRegTTest.
Defaults are L1 and L2, respectively. The dimensions of
Xlist and Ylist must be the same.
RegEQ
The prompt for the name of the Y= variable where the
calculated regression equation is to be stored. If a
Y= variable is specified, that equation is automatically
selected (turned on). The default is to store the
regression equation to the RegEQ variable only.
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421
Test and Interval Output Variables
The inferential statistics variables are calculated as indicated below. To
access these variables for use in expressions, press , 5
(5:Statistics), and then select the VARS menu listed in the last column
below.
LinRegTTest
ANOVA
VARS
Menu
Variables
Tests
p
Intervals
p-value
p
TEST
TEST
TEST
TEST
test statistics
degrees of freedom
z, t, c2, Ü
df
t, Ü
df
df
sample mean of x values for sample
1 and sample 2
v1, v2
v1, v2
sample standard deviation of x for
sample 1 and sample 2
Sx1,
Sx2
Sx1,
Sx2
TEST
TEST
number of data points for sample 1
and sample 2
n1, n2
n1, n2
pooled standard deviation
SxP
Ç
SxP
Ç
SxP
TEST
TEST
TEST
estimated sample proportion
estimated sample proportion for
population 1
Ç1
Ç1
estimated sample proportion for
population 2
Ç2
Ç2
TEST
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LinRegTTest
ANOVA
VARS
Menu
Variables
Tests
Intervals
confidence interval pair
lower,
upper
TEST
mean of x values
v
Sx
n
v
Sx
n
XY
XY
sample standard deviation of x
number of data points
standard error about the line
regression/fit coefficients
correlation coefficient
XY
s
a, b
r
TEST
EQ
EQ
coefficient of determination
regression equation
r2
EQ
RegEQ
EQ
Note: The variables listed above cannot be archived.
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Distribution Functions
DISTR menu
To display the DISTR menu, press y =.
DISTR DRAW
1:normalpdf(
2:normalcdf(
3:invNorm(
4:tpdf(
Normal probability density
Normal distribution probability
Inverse cumulative normal distribution
Student-t probability density
Student-t distribution probability
Chi-square probability density
Chi-square distribution probability
Û probability density
5:tcdf(
2
6:c pdf(
2
7:c cdf
8:Üpdf(
9:Ücdf(
Û distribution probability
0:binompdf(
A:binomcdf(
B:poissonpdf(
C:poissoncdf(
D:geometpdf(
E:geometcdf(
Binomial probability
Binomial cumulative density
Poisson probability
Poisson cumulative density
Geometric probability
Geometric cumulative density
Note: L1å99 and 1å99 specify infinity. If you want to view the area left of
upperbound, for example, specify lowerbound= L1å99.
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normalpdf(
normalpdf( computes the probability density function (pdf) for the normal
distribution at a specified x value. The defaults are mean m=0 and
standard deviation s=1. To plot the normal distribution, paste normalpdf(
to the Y= editor. The probability density function (pdf) is:
(x−µ)2
2σ
f (x) =
e−
,σ > 0
1
2
2πσ
normalpdf(x[,m,s])
Note: For this example,
Xmin = 28
Xmax = 42
Ymin = 0
Ymax = .25
Tip: For plotting the normal distribution, you can set window variables Xmin and
Xmax so that the mean m falls between them, and then select 0:ZoomFit from the
ZOOM menu.
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normalcdf(
normalcdf( computes the normal distribution probability between
lowerbound and upperbound for the specified mean m and standard
deviation s. The defaults are m=0 and s=1.
normalcdf(lowerbound,upperbound[,m,s])
invNorm(
invNorm( computes the inverse cumulative normal distribution function
for a given area under the normal distribution curve specified by mean m
and standard deviation s. It calculates the x value associated with an area
to the left of the x value. 0 area 1 must be true. The defaults are m=0
and s=1.
invNorm(area[,m,s])
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tpdf(
tpdf( computes the probability density function (pdf) for the Student-t
distribution at a specified x value. df (degrees of freedom) must be >0. To
plot the Student-t distribution, paste tpdf( to the Y= editor. The probability
density function (pdf) is:
Γ[(df +1)/2] (1+ x2/df ) − (df + 1)/2
f (x) =
Γ(df /2)
πdf
tpdf(x,df)
Note: For this example,
Xmin = L4.5
Xmax = 4.5
Ymin = 0
Ymax = .4
tcdf(
tcdf( computes the Student-t distribution probability between lowerbound
and upperbound for the specified df (degrees of freedom), which must be
> 0.
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tcdf(lowerbound,upperbound,df)
2
c pdf(
2
2
c pdf( computes the probability density function (pdf) for the c
(chi-square) distribution at a specified x value. df (degrees of freedom)
must be an integer > 0. To plot the c2 distribution, paste c2pdf( to the Y=
editor. The probability density function (pdf) is:
1
f (x) =
(1/2)df /2 xdf /2 − 1 − x/2
,x ≥ 0
e
Γ(df /2)
2
c pdf(x,df)
Note: For this example,
Xmin = 0
Xmax = 30
Ymin = L.02
Ymax = .132
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2
c cdf(
c2cdf( computes the c2 (chi-square) distribution probability between
lowerbound and upperbound for the specified df (degrees of freedom), which
must be an integer > 0.
c2cdf(lowerbound,upperbound,df)
Üpdf(
Üpdf( computes the probability density function (pdf) for the Û distribution
at a specified x value. numerator df (degrees of freedom) and denominator df
must be integers > 0. To plot the Û distribution, paste Üpdf( to the Y=
editor. The probability density function (pdf) is:
f (x) = Γ[(n + d)/2] n n/2 xn/2 − 1(1+ nx/d) − (n + d )/2,x ≥ 0
Γ(n/2)Γ(d/2)
d
where n = numerator degrees of freedom
d = denominator degrees of freedom
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Üpdf(x,numerator df,denominator df)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = 0
Ymax = 1
Ücdf(
Ücdf( computes the Û distribution probability between lowerbound and
upperbound for the specified numerator df (degrees of freedom) and
denominator df. numerator df and denominator df must be integers >0.
Ücdf(lowerbound,upperbound,numerator df,denominator df)
binompdf
binompdf( computes a probability at x for the discrete binomial
distribution with the specified numtrials and probability of success (p) on
each trial. x can be an integer or a list of integers. 0p1 must be true.
numtrials must be an integer > 0. If you do not specify x, a list of
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probabilities from 0 to numtrials is returned. The probability density
function (pdf) is:
n
x
f (x) =
px(1− p)n − x,x = 0,1,K,n
where n = numtrials
binompdf(numtrials,p[,x])
binomcdf(
binomcdf( computes a cumulative probability at x for the discrete binomial
distribution with the specified numtrials and probability of success (p) on
each trial. x can be a real number or a list of real numbers. 0p1 must
be true. numtrials must be an integer > 0. If you do not specify x, a list of
cumulative probabilities is returned.
binomcdf(numtrials,p[,x])
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poissonpdf(
poissonpdf( computes a probability at x for the discrete Poisson
distribution with the specified mean m, which must be a real number > 0.
x can be an integer or a list of integers. The probability density function
(pdf) is:
f (x) = e − µµ /x!,x = 0,1,2,ꢀ
x
poissonpdf(m,x)
poissoncdf(
poissoncdf( computes a cumulative probability at x for the discrete
Poisson distribution with the specified mean m, which must be a real
number > 0. x can be a real number or a list of real numbers.
poissoncdf(m,x)
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geometpdf(
geometpdf( computes a probability at x, the number of the trial on which
the first success occurs, for the discrete geometric distribution with the
specified probability of success p. 0p1 must be true. x can be an
integer or a list of integers. The probability density function (pdf) is:
f (x) = p(1− p)x − 1,x =1,2,ꢀ
geometpdf(p,x)
geometcdf(
geometcdf( computes a cumulative probability at x, the number of the trial
on which the first success occurs, for the discrete geometric distribution
with the specified probability of success p. 0p1 must be true. x can be
a real number or a list of real numbers.
geometcdf(p,x)
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Distribution Shading
DISTR DRAW Menu
To display the DISTR DRAW menu, press y = ~. DISTR DRAW
instructions draw various types of density functions, shade the area
specified by lowerbound and upperbound, and display the computed area
value.
To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8).
Note: Before you execute a DISTR DRAW instruction, you must set the window
variables so that the desired distribution fits the screen.
DISTR DRAW
1:ShadeNorm(
2:Shade_t(
Shades normal distribution.
Shades Student-t distribution.
Shades c2 distribution.
2
3:Shadec (
4:ShadeÛ(
Shades Û distribution.
Note: L1å99 and 1å99 specify infinity. If you want to view the area left of
upperbound, for example, specify lowerbound=L1å99.
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ShadeNorm(
ShadeNorm( draws the normal density function specified by mean m and
standard deviation s and shades the area between lowerbound and
upperbound. The defaults are m=0 and s=1.
ShadeNorm(lowerbound,upperbound[,m,s])
Note: For this example,
Xmin = 55
Xmax = 72
Ymin = L.05
Ymax = .2
Shade_t(
Shade_t( draws the density function for the Student-t distribution specified
by df (degrees of freedom) and shades the area between lowerbound and
upperbound.
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435
Shade_t(lowerbound,upperbound,df)
Note: For this example,
Xmin = L3
Xmax = 3
Ymin = L.15
Ymax = .5
Shadec2(
Shadec2( draws the density function for the c2 (chi-square) distribution
specified by df (degrees of freedom) and shades the area between
lowerbound and upperbound.
Shadec2(lowerbound,upperbound,df)
Note: For this example,
Xmin = 0
Xmax = 35
Ymin = L.025
Ymax = .1
TI-83 Plus
Inferential Statistics and Distributions
436
ShadeÜ(
ShadeÜ( draws the density function for the Û distribution specified by
numerator df (degrees of freedom) and denominator df and shades the area
between lowerbound and upperbound.
ShadeÜ(lowerbound,upperbound,numerator df,denominator df)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = L.25
Ymax = .9
TI-83 Plus
Inferential Statistics and Distributions
437
Chapter 14:
Applications
The Applications Menu
The TI-83 Plus comes with Finance and CBLàCBR applications already
listed on the APPLICATIONS menu. Except for the Finance application, you
can add and remove applications as space permits. The Finance
application is built into the TI-83 Plus code and cannot be deleted.
You can buy additional TI-83 Plus software applications that allow you to
customize further your calculator’s functionality. The calculator reserves
1.54 M of space within ROM memory specifically for applications.
Your TI-83 Plus includes Flash applications in addition to the ones
mentioned above. Press Πto see the complete list of applications
that came with your calculator.
Documentation for TI Flash applications is on the TI Resource CD. Visit
education.ti.com/guides for additional Flash application guidebooks.
TI-83 Plus
Applications
438
Getting Started: Financing a Car
Getting Started is a fast-paced introduction. Read the chapter for details.
You have found a car you would like to buy. The car costs 9,000. You can afford
payments of 250 per month for four years. What annual percentage rate (APR) will
make it possible for you to afford the car?
1. Press z † ~ ~ ~ Í to set the fixed-
decimal mode setting to 2. The TI-83 Plus will
display all numbers with two decimal places).
2. Press Œ Í to select 1:Finance from the
APPLICATIONS menu.
3. Press Í to select 1:TVM Solver from the
CALC VARS menu. The TVM Solver is displayed.
Press 48 Í to store 48 months to Ú. Press
† 9000 Í to store 9,000 to PV. Press Ì 250
Í to store L250 to PMT. (Negation indicates
cash outflow.) Press 0 Í to store 0 to FV.
TI-83 Plus
Applications
440
Press 12 Í to store 12 payments per year
to P/Y and 12 compounding periods per year to
C/Y. Setting P/Y to 12 will compute an annual
percentage rate (compounded monthly) for æ.
Press † Í to select PMT:END, which
indicates that payments are due at the end of
each period.
4. Press } } } } } } to move the cursor to
the æ prompt. Press ƒ \ to solve for
æ. What APR should you look for?
TI-83 Plus
Applications
441
Getting Started: Computing Compound
Interest
At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000
in 7 years?
Note: Because there are no payments when you solve compound interest
problems, PMT must be set to 0 and P/Y must be set to 1.
1. Press Œ Í to select 1:Finance from the
APPLICATIONS menu.
2. Press Í to select 1:TVM Solver from the
CALC VARS menu. The TVM Solver is displayed.
Press 7 to enter the number of periods in years.
Press † † Ì 1250 to enter the present value
as a cash outflow (investment). Press † 0 to
specify no payments. Press † 2000 to enter the
future value as a cash inflow (return). Press †
1 to enter payment periods per year. Press †
12 to set compounding periods per year to 12.
TI-83 Plus
Applications
442
3. Press } } } } } to place the cursor on the
æ prompt.
4. Press ƒ \ to solve for æ, the annual
interest rate.
TI-83 Plus
Applications
443
Using the TVM Solver
Using the TVM Solver
The TVM Solver displays the time-value-of-money (TVM) variables. Given
four variable values, the TVM Solver solves for the fifth variable.
PV, PMT, and FV) and P/Y and C/Y.
PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu
items Pmt_End (payment at the end of each period) and Pmt_Bgn
(payment at the beginning of each period).
To solve for an unknown TVM variable, follow these steps.
1. Press Œ Í Í to display the TVM Solver. The screen below
shows the default values with the fixed-decimal mode set to two
decimal places.
TI-83 Plus
Applications
444
2. Enter the known values for four TVM variables.
Note: Enter cash inflows as positive numbers and cash outflows as
negative numbers.
3. Enter a value for P/Y, which automatically enters the same value for
C/Y; if P/Y ƒ C/Y, enter a unique value for C/Y.
4. Select END or BEGIN to specify the payment method.
5. Place the cursor on the TVM variable for which you want to solve.
6. Press ƒ \. The answer is computed, displayed in the TVM
Solver, and stored to the appropriate TVM variable. An indicator
square in the left column designates the solution variable.
TI-83 Plus
Applications
445
Using the Financial Functions
Entering Cash Inflows and Cash Outflows
When using the TI-83 Plus financial functions, you must enter cash
inflows (cash received) as positive numbers and cash outflows (cash
paid) as negative numbers. The TI-83 Plus follows this convention when
computing and displaying answers.
FINANCE CALC Menu
To display the FINANCE CALC menu, press Œ Í.
CALC
VARS
1:TVM Solver...
2:tvm_Pmt
3:tvm_æ
4:tvm_PV
5:tvm_Ú
6:tvm_FV
7:npv(
Displays the TVM Solver.
Computes the amount of each payment.
Computes the interest rate per year.
Computes the present value.
Computes the number of payment periods.
Computes the future value.
Computes the net present value.
Computes the internal rate of return.
Computes the amortization sched. balance.
Computes the amort. sched. princ. sum.
Computes the amort. sched. interest sum.
8:irr(
9:bal(
0:GPrn(
A:GInt(
TI-83 Plus
Applications
446
CALC
VARS
B:4Nom(
Computes the nominal interest rate.
Computes the effective interest rate.
Calculates the days between two dates.
Selects ordinary annuity (end of period).
Selects annuity due (beginning of period).
C:4Eff(
D:dbd(
E:Pmt_End
F:Pmt_Bgn
Use these functions to set up and perform financial calculations on the
home screen.
TVM Solver
TI-83 Plus
Applications
447
Calculating Time Value of Money (TVM)
Calculating Time Value of Money
Use time-value-of-money (TVM) functions (menu items 2 through 6) to
analyze financial instruments such as annuities, loans, mortgages,
leases, and savings.
Each TVM function takes zero to six arguments, which must be real
numbers. The values that you specify as arguments for these functions
any TVM variable on the FINANCE VARS menu.
If you enter less than six arguments, the TI-83 Plus substitutes a
previously stored TVM variable value for each unspecified argument.
If you enter any arguments with a TVM function, you must place the
argument or arguments in parentheses.
TI-83 Plus
Applications
448
tvm_Pmt
tvm_Pmt computes the amount of each payment.
tvm_Pmt[(Ú,æ,PV,FV,P/Y,C/Y)]
Note: In the example above, the values are stored to the TVM variables in the
TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen
using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to
illustrate the effect on the payment amount.
tvm_æ
tvm_æ computes the annual interest rate.
tvm_æ[(Ú,PV,PMT,FV,P/Y,C/Y)]
TI-83 Plus
Applications
449
Calculating Cash Flows
Calculating a Cash Flow
Use the cash flow functions (menu items 7 and 8) to analyze the value of
money over equal time periods. You can enter unequal cash flows,
which can be cash inflows or outflows. The syntax descriptions for npv(
and irr( use these arguments.
•
interest rate is the rate by which to discount the cash flows (the cost of
money) over one period.
•
•
•
CF0 is the initial cash flow at time 0; it must be a real number.
CFList is a list of cash flow amounts after the initial cash flow CF0.
CFFreq is a list in which each element specifies the frequency of
occurrence for a grouped (consecutive) cash flow amount, which is
the corresponding element of CFList. The default is 1; if you enter
values, they must be positive integers < 10,000.
For example, express this uneven cash flow in lists.
4000
2000
2000
2000
4000
- 3000
TI-83 Plus
Applications
452
CF0 = 2000
CFList = {2000,L3000,4000}
CFFreq = {2,1,2}
npv(, irr(
npv( (net present value) is the sum of the present values for the cash
inflows and outflows. A positive result for npv indicates a profitable
investment.
npv(interest rate,CF0,CFList[,CFFreq])
irr( (internal rate of return) is the interest rate at which the net present
value of the cash flows is equal to zero.
irr(CF0,CFList[,CFFreq])
5000
0
3000
1000
- 2000
- 2500
TI-83 Plus
Applications
453
Calculating Amortization
Calculating an Amortization Schedule
Use the amortization functions (menu items 9, 0, and A) to calculate
balance, sum of principal, and sum of interest for an amortization
schedule.
bal(
bal( computes the balance for an amortization schedule using stored
values for æ, PV, and PMT. npmt is the number of the payment at which
you want to calculate a balance. It must be a positive integer < 10,000.
roundvalue specifies the internal precision the calculator uses to calculate
the balance; if you do not specify roundvalue, then the TI-83 Plus uses the
current Float/Fix decimal-mode setting.
bal(npmt[,roundvalue])
TI-83 Plus
Applications
454
GPrn(, GInt(
GPrn( computes the sum of the principal during a specified period for an
amortization schedule using stored values for æ, PV, and PMT. pmt1 is the
starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2
must be positive integers < 10,000. roundvalue specifies the internal
precision the calculator uses to calculate the principal; if you do not specify
roundvalue, the TI-83 Plus uses the current Float/Fix decimal-mode setting.
Note: You must enter values for æ, PV, PMT, and before computing the
principal.
GPrn(pmt1,pmt2[,roundvalue])
GInt( computes the sum of the interest during a specified period for an
amortization schedule using stored values for æ, PV, and PMT. pmt1 is the
starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2
must be positive integers < 10,000. roundvalue specifies the internal
precision the calculator uses to calculate the interest; if you do not
specify roundvalue, the TI-83 Plus uses the current Float/Fix decimal-mode
setting.
GInt(pmt1,pmt2[,roundvalue])
TI-83 Plus
Applications
455
Amortization Example: Calculating an Outstanding Loan Balance
You want to buy a home with a 30-year mortgage at 8 percent APR.
Monthly payments are 800. Calculate the outstanding loan balance after
each payment and display the results in a graph and in the table.
1. Press z. Press † ~ ~ ~ Í to set the
fixed-decimal mode setting to 2. Press † † ~
Í to select Par graphing mode.
2. Press Œ Í Í to display the
TVM Solver.
3. Press Í 360 to enter number of payments.
Press † 8 to enter the interest rate. Press † †
Ì 800 to enter the payment amount. Press † 0
to enter the future value of the mortgage. Press
† 12 to enter the payments per year, which
also sets the compounding periods per year to
12. Press † † Í to select PMT:END.
TI-83 Plus
Applications
456
4. Press } } } } } to place the cursor on the PV
prompt. Press ƒ \ to solve for the
present value.
5. Press o to display the parametric Y= editor.
Turn off all stat plots. Press „ to define X1T
as T. Press † Œ Í 9 „¤ to define
Y1T as bal(T).
6. Press p to display the window variables.
Enter the values below.
Tmin=0
Xmin=0
Ymin=0
Tmax=360
Tstep=12
Xmax=360
Xscl=50
Ymax=125000
Yscl=10000
7. Press r to draw the graph and activate the
trace cursor. Press ~ and | to explore the
graph of the outstanding balance over time.
Press a number and then press Í to view
the balance at a specific time T.
8. Press y - and enter the values below.
TblStart=0
@Tbl=12
TI-83 Plus
Applications
457
9. Press y 0 to display the table of
outstanding balances (Y1T).
10.Press z † † † † † † † ~ ~ Í to
select G.T split-screen mode, in which the
graph and table are displayed simultaneously.
Press r to display X1T (time) and Y1T
(balance) in the table.
TI-83 Plus
Applications
458
Calculating Interest Conversion
Calculating an Interest Conversion
Use the interest conversion functions (menu items B and C) to convert
interest rates from an annual effective rate to a nominal rate (4Nom( ) or
from a nominal rate to an annual effective rate (4Eff( ).
4Nom(
4Nom( computes the nominal interest rate. effective rate and compounding
periods must be real numbers. compounding periods must be >0.
4Nom(effective rate,compounding periods)
4Eff(
4Eff( computes the effective interest rate. nominal rate and compounding
periods must be real numbers. compounding periods must be >0.
4Eff(nominal rate,compounding periods)
TI-83 Plus
Applications
459
Finding Days between Dates/Defining
Payment Method
dbd(
Use the date function dbd( (menu item D) to calculate the number of days
between two dates using the actual-day-count method. date1 and date2
can be numbers or lists of numbers within the range of the dates on the
standard calendar.
Note: Dates must be between the years 1950 through 2049.
dbd(date1,date2)
You can enter date1 and date2 in either of two formats.
• MM.DDYY (United States)
• DDMM.YY (Europe)
The decimal placement differentiates the date formats.
TI-83 Plus
Applications
460
Defining the Payment Method
Pmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an
ordinary annuity or an annuity due. When you execute either command,
the TVM Solver is updated.
Pmt_End
Pmt_End (payment end) specifies an ordinary annuity, where payments
occur at the end of each payment period. Most loans are in this category.
Pmt_End is the default.
Pmt_End
On the TVM Solver’s PMT:END BEGIN line, select END to set PMT to
ordinary annuity.
Pmt_Bgn
Pmt_Bgn (payment beginning) specifies an annuity due, where payments
occur at the beginning of each payment period. Most leases are in this
category.
Pmt_Bgn
On the TVM Solver’s PMT:END BEGIN line, select BEGIN to set PMT to
annuity due.
TI-83 Plus
Applications
461
Using the TVM Variables
FINANCE VARS Menu
To display the FINANCE VARS menu, press Œ Í ~. You can use
TVM variables in TVM functions and store values to them on the home
screen.
CALCVARS
1:Ú
Total number of payment periods
Annual interest rate
2:æ
3:PV
4:PMT
5:FV
6:P/Y
7:C/Y
Present value
Payment amount
Future value
Number of payment periods per year
Number of compounding periods/year
Ú, æ, PV, PMT, FV
Ú, æ, PV, PMT, and FV are the five TVM variables. They represent the
elements of common financial transactions, as described in the table
above. æ is an annual interest rate that is converted to a per-period rate
based on the values of P/Y and C/Y.
TI-83 Plus
Applications
462
P/Y and C/Y
P/Y is the number of payment periods per year in a financial transaction.
C/Y is the number of compounding periods per year in the same
transaction.
When you store a value to P/Y, the value for C/Y automatically changes
to the same value. To store a unique value to C/Y, you must store the
value to C/Y after you have stored a value to P/Y.
TI-83 Plus
Applications
463
The CBL/CBR Application
The CBL/CBR application allows you to collect real world data. The
TI-83 Plus comes with the CBLàCBR application already listed on the
APPLICATIONS menu (9 2).
Steps for Running the CBLàCBR Application
Follow these basic steps when using the CBLàCBR application. You may
not have to do all of them each time.
Press 9 2.
Select the CBLàCBR
application.
Press b.
Press 1, 2, or 3.
Specify the data collection
method.
TI-83 Plus
Applications
464
Highlight options
or enter value and
press b.
Select options, if
applicable.
Collect the data.
Follow directions, if
applicable.
Select Go… or
START NOW.
Stop the data collection, if
necessary. Repeat these
steps or exit the
Press ^ and
° or ±.
APPLICATIONS menu.
TI-83 Plus
Applications
465
Selecting the CBL/CBR Application
To use a CBL/CBR application, you need a CBL 2/CBL or CBR (as
applicable), a TI-83 Plus, and a unit-to-unit link cable.
1. Press Œ.
2. Select 2:CBL/CBR to set up the TI-83 Plus to
use either of the applications. An informational
screen appears first.
3. Press any key to continue to the next menu.
TI-83 Plus
Applications
466
Data Collection Methods and Options
Specifying the Data Collection Method from the CBL/CBR APP
Menu
With a CBL 2/CBL or CBR, you can collect data in one of three ways: GAUGE
(bar or meter), DATA LOGGER (a Temp-Time, Light-Time, Volt-Time, or
Sonic-Time graph), or RANGER, which runs the RANGER program, the
built-in CBR data collection program.
The CBL/CBR APP menu contains the following data collection methods:
CBL/CBR APP:
1:GAUGE
Displays results as either a bar or meter.
2:DATA LOGGER
Displays results as a Temp-Time, Light-Time, Volt-Time, or
Sonic-Time graph.
3:RANGER
4:QUIT
Sets up and runs the RANGER program.
Quits the CBLàCBR application.
Note: CBL 2/CBL and CBR differ in that CBL 2/CBL allows you to collect data using
one of several different probes including: Temp (Temperature), Light, Volt
(Voltage), or Sonic. CBR collects data using only the built-in Sonic probe. You
can find more information on CBL 2/CBL and CBR in their user manuals.
TI-83 Plus
Applications
467
Specifying Options for Each Data Collection Method
After you select a data collection method from the CBL/CBR APP menu, a
screen showing the options for that method is displayed. The method
you choose, as well as the data collection options you choose for that
method, determine whether you use the CBR or the CBL 2/CBL. Refer to
the charts in the following sections to find the options for the application
you are using.
GAUGE
The GAUGE data collection method lets you choose one of four different
probes: temp, Light, Volt, or Sonic.
1. Press Œ 2 Í.
2. Select 1:GAUGE.
3. Select options.
TI-83 Plus
Applications
468
When you select a probe option, all other options change accordingly.
Use " and ! to move between the probe options. To select a probe,
highlight the one you want with the cursor keys, and then press Í.
GAUGE Options (Defaults)
Probe:
Type:
Min:
Temp
Light
Volt
Sonic
Bar or Meter
0
0
1
M10
10
0
Max:
100
6
Units:
2
¡C or ¡F
mWàcm
Volt
m or Ft
Directions:
On or Off
TYPE
The GAUGE data collection results are represented according to TYPE: Bar
or Meter. Highlight the one you want with the cursor keys, and then press
Í.
TI-83 Plus
Applications
469
Bar
Meter
MIN and MAX
MIN and MAX refer to the minimum and maximum UNIT values for the
specified probe. Defaults are listed in the Gauge Options table. See the
CBL 2/CBL and CBR guidebook for specific MINàMAX ranges. Enter
values using the number keys.
UNITS
The results are displayed according to the UNITS specified. To specify a
unit measurement (Temp or Sonic probes only), highlight the one you
want using the cursor keys, enter a value using the number keys, and
then press Í.
TI-83 Plus
Applications
470
DIRECTNS (Directions)
If DIRECTNS=On, the calculator displays step-by-step directions on the
screen, which help you set up and run the data collection. To select On
or Off, highlight the one you want with the cursor keys, and then press
Í.
With the Sonic data collection probe, if DIRECTNS=On, the calculator
displays a menu screen before starting the application asking you to
select 1:CBL or 2:CBR. This ensures that you get the appropriate
directions. Press 1 to specify CBL 2/CBL or 2 to specify CBR.
Data Collection Comments and Results
To label a specific data point, press Í to pause the data collection.
You will see a Reference#: prompt. Enter a number using the number
keys. The calculator automatically converts the reference numbers and
the corresponding results into list elements using the following list names
(you cannot rename these lists):
Probe
Temp
Light
Volt
Comment Labels (X) Stored to:
Data Results (Y) Stored to:
ÙTREF
ÙLREF
ÙVREF
ÙDREF
ÙTEMP
ÙLIGHT
ÙVOLT
ÙDIST
Sonic
TI-83 Plus
Applications
471
To see all elements in one of these lists, you can insert these lists into
the List editor just as you would any other list. Access list names from
the - 9 NAMES menu.
Note: These lists are only temporary placeholders for comment labels and data
results for any particular probe. Therefore, every time you collect data and enter
comments for one of the four probes, the two lists pertaining to that probe are
overwritten with comment labels and data results from the most recently
collected data..
If you want to save comment labels and data results from more than one
data collection, copy all list elements that you want to save to a list with a
different name.
Also, the DATA LOGGER data collection method stores data results to the
same list names, overwriting previously-collected data results, even
those collected using the GAUGE data collection method.
TI-83 Plus
Applications
472
DATA LOGGER
1. Press Œ 2 Í.
2. Select 2:DATA LOGGER.
The DATA LOGGER data collection method lets you choose one of four
different probes: Temp, Light, Volt, or Sonic. You can use the CBL 2/CBL
with all probes; you can use the CBR only with the Sonic probe.
When you select a probe option, all other options change accordingly.
Use " and ! to move between the probe options. To select a probe,
highlight the one you want with the cursor keys, and then press Í.
TI-83 Plus
Applications
473
DATA LOGGER Options (Defaults)
Temp
Light
Volt
Sonic
99
#SAMPLES:
99
99
99
INTRVL
(SEC):
1
1
1
1
2
UNITS:
¡C or ¡F
mW/cm
Volt
Cm or Ft
PLOT:
RealTme or End
On or Off
DIRECTNS:
Ymin
('):
0
0
1
M10
0
6
Ymax
('):
100
10
The DATA LOGGER data collection results are represented as a
Temp-Time, Light-Time, Volt-Time, or Distance-Time graph.
A Distance-Time graph in
meters (Sonic probe).
TI-83 Plus
Applications
474
#SAMPLES
#SAMPLES refers to how many data samples are collected and then
graphed. For example, if #SAMPLES=99, data collection stops after the
99th sample is collected. Enter values using the number keys.
INTRVL (SEC)
INTRVL (SEC) specifies the interval in seconds between each data sample
that is collected. For example, if you want to collect 99 samples and
INTRVL=1, it takes 99 seconds to finish data collection. Enter values using
the number keys. See the CBL 2/CBL or CBR guidebook for more
information about interval limits.
UNITS
The results are displayed according to the UNITS specified. To specify a
unit measurement (Temp or Sonic only), highlight the one you want using
the cursor keys, and then press Í.
TI-83 Plus
Applications
475
PLOT
You can specify whether you want the calculator to collect realtime
(RealTme) samples, which means that the calculator graphs data points
immediately as they are being collected, or you can wait and show the
graph only after all data points have been collected (End). Highlight the
option you want with the cursor keys, and then press Í.
Ymin and Ymax
To specify Ymin and Ymax values for the final graph, press p to view
the PLOT WINDOW screen. Use $ and # to move between options. Enter
Ymin and Ymax using the number keys. Press - l to return to the
DATA LOGGER options screen.
DIRECTNS (Directions)
If DIRECTNS=On, the calculator displays step-by-step directions on the
screen, which help you set up and run the data collection. To select On
or Off, highlight the one you want with the cursor keys, and then press
b.
With the Sonic data collection probe, if DIRECTNS=On, the calculator
displays a menu screen before starting the application asking you to
select 1:CBL or 2:CBR. This ensures that you get the appropriate
directions. Press 1 to specify CBL 2/CBL or 2 to specify CBR.
TI-83 Plus
Applications
476
Data Collection Results
The calculator automatically converts all collected data points into list
elements using the following list names (you cannot rename the lists):
Probe
Temp
Light
Volt
Time Values (X) stored to:
¨TTEMP
Data Results (Y) Stored to:
¨TEMP
¨LIGHT
¨VOLT
¨DIST
¨TLGHT
¨TVOLT
Sonic
¨TDIST
To see all elements in one of these lists, you can insert these lists into
the List editor just as you would any other list. Access list names from
the - 9 NAMES menu.
Note: These lists are only temporary placeholders for data results for any
particular probe. Therefore, every time you collect data for one of the four
probes, the list pertaining to that probe is overwritten with data results from the
most recently collected data.
If you want to save data results from more than one data collection, copy
all list elements that you want to save to a list with a different name.
Also, the GAUGE data collection method stores data results to the same
list names, overwriting previously-collected data results, even those
collected using the DATA LOGGER data collection method.
TI-83 Plus
Applications
477
RANGER
Selecting the RANGER data collection method runs the CBR RANGER
program, a customized program especially for the TI-83 Plus that makes
it compatible with the CBR. When the collection process is halted, the
CBR RANGER is deleted from RAM. To run the CBR RANGER program
again, press Πand select the CBL/CBR application.
Note: The Ranger data collection method only uses the Sonic probe.
1. Press 9 2 b.
2. Select 3:RANGER.
3. Press b.
4. Select options.
For detailed information about the RANGER program as well as option
TI-83 Plus
Applications
478
Starting Data Collection
Collecting the Data
After you specify all of the options for your data collection method, select
the Go option from the GAUGE or DATA LOGGER options screen. If you are
using the RANGER data collection method, select 1:SETUPàSAMPLE from the
MAIN menu, and then START NOW.
• If DIRECTNS=Off, GAUGE and DATA LOGGER data collection begin
immediately.
• If DIRECTNS=On, the calculator displays step-by-step directions.
If PROBE=Sonic, the calculator first displays a menu screen asking you to
select 1:CBL or 2:CBR. This ensures that you get the appropriate
directions. Press 1 to specify CBL 2/CBL or 2 to specify CBR.
If you select START NOW from the MAIN menu of the RANGER data
collection method, the calculator displays one directions screen. Press
b to begin data collection.
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Applications
479
Stopping Data Collection
To stop the GAUGE data collection method, press : on the
TI-83 Plus.
The DATA LOGGER and RANGER data collection methods stop after the
specified number of samples have been collected. To stop them before
this happens:
1. Press ^ on the TI-83 Plus.
2. Press ¤ on the CBR, T on the CBL 2, or P on the
CBL.
To exit from the GAUGE or DATA LOGGER option menus without beginning
data collection, press - l.
To exit from the RANGER option menu without beginning data collection,
select MAIN menu. Select 6:QUIT to return to the CBLàCBR APP menu.
Press 4:QUIT from the CBLàCBR APP menu to return to the TI-83 Plus
Home screen.
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Applications
480
Chapter 15:
CATALOG, Strings, Hyperbolic
Functions
Browsing the TI-83 Plus CATALOG
What Is the CATALOG?
The CATALOG is an alphabetical list of all functions and instructions on the
TI-83 Plus. You also can access each CATALOG item from a menu or the
keyboard, except:
• The six string functions
• The six hyperbolic functions
• The solve( instruction without the equation solver editor (Chapter 2)
• The inferential stat functions without the inferential stat editors
(Chapter 13)
Note: The only CATALOG programming commands you can execute from the
home screen are GetCalc(, Get(, and Send(.
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481
Selecting an Item from the CATALOG
To select a CATALOG item, follow these steps.
1. Press y ãCATALOGä to display the CATALOG.
The 4 in the first column is the selection cursor.
2. Press † or } to scroll the CATALOG until the selection cursor points to
the item you want.
• To jump to the first item beginning with a particular letter, press
that letter; alpha-lock is on.
• Items that begin with a number are in alphabetical order according
to the first letter after the number. For example, 2.PropZTest( is
among the items that begin with the letter P.
• Functions that appear as symbols, such as +, L1, <, and ‡(, follow
the last item that begins with Z. To jump to the first symbol, !,
press [q].
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482
3. Press Í to paste the item to the current screen.
Tip: From the top of the CATALOG menu, press } to move to the bottom. From
the bottom, press † to move to the top.
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CATALOG, Strings, Hyperbolic Functions
483
Entering and Using Strings
What Is a String?
A string is a sequence of characters that you enclose within quotation
marks. On the TI-83 Plus, a string has two primary applications.
• It defines text to be displayed in a program.
• It accepts input from the keyboard in a program.
Characters are the units that you combine to form a string.
• Count each number, letter, and space as one character.
• Count each instruction or function name, such as sin( or cos(, as one
character; the TI-83 Plus interprets each instruction or function name
as one character.
Entering a String
To enter a string on a blank line on the home screen or in a program,
follow these steps.
1. Press ƒ [ã] to indicate the beginning of the string.
2. Enter the characters that comprise the string.
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484
• Use any combination of numbers, letters, function names, or
instruction names to create the string.
• To enter a blank space, press ƒ ['].
• To enter several alpha characters in a row, press y 7 to
activate alpha-lock.
3. Press ƒ [ã] to indicate the end of the string.
"string"
4. Press Í. On the home screen, the string is displayed on the next
line without quotations. An ellipsis (...) indicates that the string continues
beyond the screen. To scroll the entire string, press ~ and |.
Note: Quotation marks do not count as string characters.
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485
Storing Strings to String Variables
String Variables
The TI-83 Plus has 10 variables to which you can store strings. You can
use string variables with string functions and instructions.
To display the VARS STRING menu, follow these steps.
1. Press to display the VARS menu. Move the cursor to 7:String.
2. Press Í to display the STRING secondary menu.
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486
Storing a String to a String Variable
To store a string to a string variable, follow these steps.
1. Press ƒ [ã], enter the string, and press ƒ [ã].
2. Press ¿.
3. Press 7 to display the VARS STRING menu.
4. Select the string variable (from Str1 to Str9, or Str0) to which you want
to store the string.
The string variable is pasted to the current cursor location, next to the
store symbol (!).
5. Press Í to store the string to the string variable. On the home
screen, the stored string is displayed on the next line without
quotation marks.
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487
String Functions and Instructions in the
CATALOG
Displaying String Functions and Instructions in the CATALOG
String functions and instructions are available only from the CATALOG.
The table below lists the string functions and instructions in the order in
which they appear among the other CATALOG menu items. The ellipses in
the table indicate the presence of additional CATALOG items.
CATALOG
...
Equ4String(
expr(
Converts an equation to a string.
Converts a string to an expression.
...
inString(
...
Returns a character’s place number.
Returns a string’s character length.
length(
...
String4Equ(
sub(
Converts a string to an equation.
Returns a string subset as a string.
...
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489
+ (Concatenation)
To concatenate two or more strings, follow these steps.
1. Enter string1, which can be a string or string name.
2. Press Ã.
3. Enter string2, which can be a string or string name. If necessary,
press à and enter string3, and so on.
string1+string2+string3. . .
4. Press Í to display the strings as a single string.
Selecting a String Function from the CATALOG
To select a string function or instruction and paste it to the current
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490
Equ4String(
Equ4String( converts to a string an equation that is stored to any VARS
Y.VARS variable. Yn contains the equation. Strn (from Str1 to Str9, or Str0)
is the string variable to which you want the equation to be stored as a
string.
Equ4String(Yn,Strn)
expr(
expr( converts the character string contained in string to an expression
and executes it. string can be a string or a string variable.
expr(string)
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491
inString(
inString( returns the character position in string of the first character of
substring. string can be a string or a string variable. start is an optional
character position at which to start the search; the default is 1.
inString(string,substring[,start])
Note: If string does not contain substring, or start is greater than the length of
string, inString( returns 0.
length(
length( returns the number of characters in string. string can be a string or
string variable.
Note: An instruction or function name, such as sin( or cos(, counts as one
character.
length(string)
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492
String4Equ(
String4Equ( converts string into an equation and stores the equation to Yn.
string can be a string or string variable. String4Equ( is the inverse of
Equ4String(.
String4Equ(string,Yn)
sub(
sub( returns a string that is a subset of an existing string. string can be a
string or a string variable. begin is the position number of the first
character of the subset. length is the number of characters in the subset.
sub(string,begin,length)
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493
Hyperbolic Functions in the CATALOG
Hyperbolic Functions
The hyperbolic functions are available only from the CATALOG. The table
below lists the hyperbolic functions in the order in which they appear
among the other CATALOG menu items. The ellipses in the table indicate
the presence of additional CATALOG items.
CATALOG
...
cosh(
Hyperbolic cosine
Hyperbolic arccosine
L1
cosh
...
(
(
(
sinh(
Hyperbolic sine
Hyperbolic arcsine
L1
sinh
...
tanh(
Hyperbolic tangent
Hyperbolic arctangent
L1
tanh
...
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CATALOG, Strings, Hyperbolic Functions
495
sinh(, cosh(, tanh(
sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real
numbers, expressions, and lists.
sinh(value)
cosh(value)
tanh(value)
sinhL1(, coshL1(, tanhL1(
L1
L1
sinh ( is the hyperbolic arcsine function. cosh ( is the hyperbolic
L1
arccosine function. tanh ( is the hyperbolic arctangent function. Each is
valid for real numbers, expressions, and lists.
L1
sinh (value)
L1
cosh (value)
L1
sinh (value)
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496
Chapter 16:
Programming
Getting Started: Volume of a Cylinder
Getting Started is a fast-paced introduction. Read the chapter for details.
A program is a set of commands that the TI-83 Plus executes sequentially, as if
you had entered them from the keyboard. Create a program that prompts for the
radius R and the height H of a cylinder and then computes its volume.
1. Press ~ ~ to display the PRGM NEW
menu.
2. Press Í to select 1:Create New. The Name=
prompt is displayed, and alpha-lock is on. Press
[C] [Y] [L] [I] [N] [D] [E] [R], and then press Í to
name the program CYLINDER.
You are now in the program editor. The colon
( : ) in the first column of the second line
indicates the beginning of a command line.
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Programming
497
3. Press ~ 2 to select 2:Prompt from the
PRGM I/O menu. Prompt is copied to the
command line. Press ƒ [R] ¢ ƒ [H] to
enter the variable names for radius and height.
Press Í.
4. Press y ãpä ƒ [R] ¡ ƒ [H] ¿
ƒ [V] Í to enter the expression pR2H
and store it to the variable V.
5. Press ~ 3 to select 3:Disp from the PRGM
I/O menu. Disp is pasted to the command line.
Press y 7 ããä [V] [O] [L] [U] [M] [E]['] [I] [S]
ããä ƒ ¢ ƒ [V] Í to set up the
program to display the text VOLUME IS on one
line and the calculated value of V on the next.
6. Press y 5 to display the home screen.
7. Press to display the PRGM EXEC menu. The
items on this menu are the names of stored
programs.
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Programming
498
8. Press Í to paste prgmCYLINDER to the
current cursor location. (If CYLINDER is not item
1 on your PRGM EXEC menu, move the cursor to
CYLINDER before you press Í.)
9. Press Í to execute the program. Enter 1.5
for the radius, and then press Í. Enter 3 for
the height, and then press Í. The text
VOLUME IS, the value of V, and Done are
displayed.
Repeat steps 7 through 9 and enter different
values for R and H.
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Programming
499
Creating and Deleting Programs
What Is a Program?
A program is a set of one or more command lines. Each line contains
one or more instructions. When you execute a program, the TI-83 Plus
performs each instruction on each command line in the same order in
which you entered them. The number and size of programs that the
TI-83 Plus can store is limited only by available memory.
Creating a New Program
To create a new program, follow these steps.
1. Press | to display the PRGM NEW menu.
2. Press Í to select 1:Create New. The Name= prompt is displayed,
and alpha-lock is on.
3. Press a letter from A to Z or q to enter the first character of the new
program name.
Note: A program name can be one to eight characters long. The first
character must be a letter from A to Z or q. The second through eighth
characters can be letters, numbers, or q.
TI-83 Plus
Programming
500
4. Enter zero to seven letters, numbers, or q to complete the new
program name.
5. Press Í. The program editor is displayed.
6. Enter one or more program commands.
7. Press y 5 to leave the program editor and return to the home
screen.
Managing Memory and Deleting a Program
To check whether adequate memory is available for a program you want
to enter:
1. Press y L to display the MEMORY menu.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE
menu (Chapter 18).
3. Select 7:Prgm to display the PRGM editor.
The TI-83 Plus expresses memory quantities in bytes.
TI-83 Plus
Programming
501
You can increase available memory in one of two ways. You can delete
one or more programs or you can archive some programs.
To increase available memory by deleting a specific program:
1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY
menu.
2. Select 7:Prgm to display the PRGM editor (Chapter 18).
3. Press } and † to move the selection cursor (4) next to the program
you want to delete, and then press {. The program is deleted from
memory.
Note: You will receive a message asking you to confirm this delete action.
Select 2:yes to continue.
To leave the PRGM editor screen without deleting anything, press
y 5, which displays the home screen.
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Programming
502
To increase available memory by archiving a program:
1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY
menu.
2. Select 2:Mem Mgmt/Del to display the MEM MGMT/DEL menu.
3. Select 7:Prgm... to display the PRGM menu.
4. Press Í to archive the program. An asterisk will appear to the left
of the program to indicate it is an archived program.
To unarchive a program in this screen, put the cursor next to the
archived program and press Í. The asterisk will disappear.
Note: Archive programs cannot be edited or executed. In order to edit or
execute an archived program, you must first unarchive it.
TI-83 Plus
Programming
503
Entering Command Lines and Executing
Programs
Entering a Program Command Line
You can enter on a command line any instruction or expression that you
could execute from the home screen. In the program editor, each new
command line begins with a colon. To enter more than one instruction or
expression on a single command line, separate each with a colon.
Note: A command line can be longer than the screen is wide; long command
lines wrap to the next screen line.
While in the program editor, you can display and select from menus. You
can return to the program editor from a menu in either of two ways.
• Select a menu item, which pastes the item to the current command line.
• Press ‘.
When you complete a command line, press Í. The cursor moves to
the next command line.
Programs can access variables, lists, matrices, and strings saved in
memory. If a program stores a new value to a variable, list, matrix, or
string, the program changes the value in memory during execution.
You can call another program as a subroutine.
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Programming
504
Executing a Program
To execute a program, begin on a blank line on the home screen and
follow these steps.
1. Press to display the PRGM EXEC menu.
2. Select a program name from the PRGM EXEC menu. prgmname is
pasted to the home screen (for example, prgmCYLINDER).
3. Press Í to execute the program. While the program is executing,
the busy indicator is on.
Last Answer (Ans) is updated during program execution. Last Entry is
not updated as each command is executed (Chapter 1).
The TI-83 Plus checks for errors during program execution. It does not
check for errors as you enter a program.
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Programming
505
Editing Programs
Editing a Program
To edit a stored program, follow these steps.
1. Press ~ to display the PRGM EDIT menu.
2. Select a program name from the PRGM EDIT menu. Up to the first
seven lines of the program are displayed.
Note: The program editor does not display a $ to indicate that a program
continues beyond the screen.
3. Edit the program command lines.
• Move the cursor to the appropriate location, and then delete,
overwrite, or insert.
• Press ‘ to clear all program commands on the command line
(the leading colon remains), and then enter a new program
command.
Tip: To move the cursor to the beginning of a command line, press y |; to
move to the end, press y ~. To scroll the cursor down seven command lines,
press ƒ †. To scroll the cursor up seven command lines, press ƒ }.
TI-83 Plus
Programming
507
Inserting and Deleting Command Lines
To insert a new command line anywhere in the program, place the
cursor where you want the new line, press y 6, and then press
Í. A colon indicates a new line.
To delete a command line, place the cursor on the line, press ‘ to
clear all instructions and expressions on the line, and then press { to
delete the command line, including the colon.
TI-83 Plus
Programming
508
Copying and Renaming Programs
Copying and Renaming a Program
To copy all command lines from one program into a new program, follow
steps.
1. Press y K. Rcl is displayed on the bottom line of the program
editor in the new program (Chapter 1).
2. Press | to display the PRGM EXEC menu.
3. Select a name from the menu. prgmname is pasted to the bottom line
of the program editor.
4. Press Í. All command lines from the selected program are
copied into the new program.
Copying programs has at least two convenient applications.
• You can create a template for groups of instructions that you use
frequently.
• You can rename a program by copying its contents into a new
program.
TI-83 Plus
Programming
509
Note: You also can copy all the command lines from one existing program to
another existing program using RCL.
Scrolling the PRGM EXEC and PRGM EDIT Menus
The TI-83 Plus sorts PRGM EXEC and PRGM EDIT menu items automatically
into alphanumerical order. Each menu only labels the first 10 items using
1 through 9, then 0.
To jump to the first program name that begins with a particular alpha
character or q, press ƒ [letter from A to Z or q].
Tip: From the top of either the PRGM EXEC or PRGM EDIT menu, press } to
move to the bottom. From the bottom, press † to move to the top. To scroll the
cursor down the menu seven items, press ƒ †. To scroll the cursor up the
menu seven items, press ƒ }.
TI-83 Plus
Programming
510
PRGM CTL (Control) Instructions
PRGM CTL Menu
To display the PRGM CTL (program control) menu, press from the
program editor only.
CTL I/O EXEC
1:If
Creates a conditional test.
2:Then
Executes commands when If is true.
Executes commands when If is false.
Creates an incrementing loop.
Creates a conditional loop.
3:Else
4:For(
5:While
6:Repeat
7:End
Creates a conditional loop.
Signifies the end of a block.
Pauses program execution.
Defines a label.
8:Pause
9:Lbl
0:Goto
Goes to a label.
A:IS>(
Increments and skips if greater than.
Decrements and skips if less than.
Defines menu items and branches.
Executes a program as a subroutine.
Returns from a subroutine.
B:DS<(
C:Menu(
D:prgm
E:Return
F:Stop
Stops execution.
G:DelVar
H:GraphStyle(
Deletes a variable from within program.
Designates the graph style to be drawn.
TI-83 Plus
Programming
511
These menu items direct the flow of an executing program. They make it
easy to repeat or skip a group of commands during program execution.
When you select an item from the menu, the name is pasted to the
cursor location on a command line in the program.
To return to the program editor without selecting an item, press ‘.
Controlling Program Flow
Program control instructions tell the TI-83 Plus which command to
execute next in a program. If, While, and Repeat check a defined
condition to determine which command to execute next. Conditions
frequently use relational or Boolean tests (Chapter 2), as in:
If A<7:A+1!A
or
If N=1 and M=1:Goto Z
If
Use If for testing and branching. If condition is false (zero), then the
command immediately following If is skipped. If condition is true (nonzero),
then the next command is executed. If instructions can be nested.
TI-83 Plus
Programming
512
Program
Output
If.Then.Else
Else following If.Then executes a group of commands if condition is false
(zero). End identifies the end of the group of commands.
:If condition
:Then
:command (if true)
:command (if true)
:Else
:command (if false)
:command (if false)
:End
:command
TI-83 Plus
Programming
514
Program
Output
For(
For( loops and increments. It increments variable from begin to end by
increment. increment is optional (default is 1) and can be negative
(end<begin). end is a maximum or minimum value not to be exceeded. End
identifies the end of the loop. For( loops can be nested.
:For(variable,begin,end[,increment])
:command (while end not exceeded)
:command (while end not exceeded)
:End
:command
TI-83 Plus
Programming
515
Program
While
Output
While performs a group of commands while condition is true. condition is
frequently a relational test (Chapter 2). condition is tested when While is
encountered. If condition is true (nonzero), the program executes a group
of commands. End signifies the end of the group. When condition is false
(zero), the program executes each command following End. While
instructions can be nested.
:While condition
:command (while condition is true)
:command (while condition is true)
:End
:command
TI-83 Plus
Programming
516
Program
Repeat
Output
Repeat repeats a group of commands until condition is true (nonzero). It is
similar to While, but condition is tested when End is encountered;
therefore, the group of commands is always executed at least once. Repeat
instructions can be nested.
:Repeat condition
:command (until condition is true)
:command (until condition is true)
:End
:command
Program
Output
TI-83 Plus
Programming
517
End
End identifies the end of a group of commands. You must include an End
instruction at the end of each For(, While, or Repeat loop. Also, you must
paste an End instruction at the end of each If.Then group and each
If.Then.Else group.
Pause
Pause suspends execution of the program so that you can see answers
or graphs. During the pause, the pause indicator is on in the top-right
corner. Press Í to resume execution.
•
Pause without a value temporarily pauses the program. If the
DispGraph or Disp instruction has been executed, the appropriate
screen is displayed.
•
Pause with value displays value on the current home screen. value can
be scrolled.
Pause [value]
TI-83 Plus
Programming
518
Program
Output
Lbl, Goto
Lbl (label) and Goto (go to) are used together for branching.
Lbl specifies the label for a command. label can be one or two characters
(A through Z, 0 through 99, or q).
Lbl label
Goto causes the program to branch to label when Goto is encountered.
Goto label
TI-83 Plus
Programming
519
Program
Output
IS>(
IS>( (increment and skip) adds 1 to variable. If the answer is > value (which
can be an expression), the next command is skipped; if the answer is {
value, the next command is executed. variable cannot be a system variable.
:IS>(variable,value)
:command (if answer value)
:command (if answer > value)
Program
Output
Note: IS>( is not a looping instruction.
TI-83 Plus
Programming
520
DS<(
DS<( (decrement and skip) subtracts 1 from variable. If the answer is
< value (which can be an expression), the next command is skipped; if the
answer is | value, the next command is executed. variable cannot be a
system variable.
:DS<(variable,value)
:command (if answer ‚ value)
:command (if answer < value)
Program
Output
Note: DS<( is not a looping instruction.
Menu(
Menu( sets up branching within a program. If Menu( is encountered during
program execution, the menu screen is displayed with the specified
menu items, the pause indicator is on, and execution pauses until you
select a menu item.
TI-83 Plus
Programming
521
The menu title is enclosed in quotation marks ( " ). Up to seven pairs of
menu items follow. Each pair comprises a text item (also enclosed in
quotation marks) to be displayed as a menu selection, and a label item to
which to branch if you select the corresponding menu selection.
Menu("title","text1",label1,"text2",label2, . . .)
Program
Output
The program above pauses until you select 1 or 2. If you select 2, for
example, the menu disappears and the program continues execution at
Lbl B.
prgm
Use prgm to execute other programs as subroutines. When you select
prgm, it is pasted to the cursor location. Enter characters to spell a
program name. Using prgm is equivalent to selecting existing programs
from the PRGM EXEC menu; however, it allows you to enter the name of a
program that you have not yet created.
prgmname
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Programming
522
Note: You cannot directly enter the subroutine name when using RCL. You
must paste the name from the PRGM EXEC menu.
Return
Return quits the subroutine and returns execution to the calling program,
even if encountered within nested loops. Any loops are ended. An
implied Return exists at the end of any program that is called as a
subroutine. Within the main program, Return stops execution and returns
to the home screen.
Stop
Stop stops execution of a program and returns to the home screen. Stop
is optional at the end of a program.
DelVar
DelVar deletes from memory the contents of variable.
DelVar variable
TI-83 Plus
Programming
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GraphStyle(
GraphStyle( designates the style of the graph to be drawn. function# is the
number of the Y= function name in the current graphing mode. graphstyle
is a number from 1 to 7 that corresponds to the graph style, as shown
below.
1 = ç (line)
2 = è (thick)
3 = é (shade above)
4 = ê (shade below)
5 = ë (path)
6 = ì (animate)
7 = í (dot)
GraphStyle(function#,graphstyle)
For example, GraphStyle(1,5) in Func mode sets the graph style for Y1 to
ë (path; 5).
Not all graph styles are available in all graphing modes. For a detailed
description of each graph style, see the Graph Styles table in Chapter 3.
TI-83 Plus
Programming
524
PRGM I/O (Input/Output) Instructions
PRGM I/O Menu
To display the PRGM I/O (program input/output) menu, press ~ from
within the program editor only.
CTL I/O EXEC
1:Input
Enters a value or uses the cursor.
Prompts for entry of variable values.
Displays text, value, or the home screen.
Displays the current graph.
2:Prompt
3:Disp
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHome
9:ClrTable
0:GetCalc(
A:Get(
Displays the current table.
Displays text at a specified position.
Checks the keyboard for a keystroke.
Clears the display.
Clears the current table.
Gets a variable from another TI-83 Plus.
Gets a variable from CBL 2™/CBL™ or CBR™.
Sends a variable to CBL 2/CBL or CBR.
B:Send(
These instructions control input to and output from a program during
execution. They allow you to enter values and display answers during
program execution.
To return to the program editor without selecting an item, press ‘.
TI-83 Plus
Programming
525
Storing a Variable Value with Input
Input with variable displays a ? (question mark) prompt during execution.
variable may be a real number, complex number, list, matrix, string, or Y=
function. During program execution, enter a value, which can be an
expression, and then press Í. The value is evaluated and stored to
variable, and the program resumes execution.
Input [variable]
You can display text or the contents of Strn (a string variable) of up to 16
characters as a prompt. During program execution, enter a value after
the prompt and then press Í. The value is stored to variable, and the
program resumes execution.
Input ["text",variable]
Input [Strn,variable]
Program
Output
TI-83 Plus
Programming
527
Note: When a program prompts for input of lists and Yn functions during
execution, you must include the braces ( { } ) around the list elements and
quotation marks ( " ) around the expressions.
Prompt
During program execution, Prompt displays each variable, one at a time,
followed by =?. At each prompt, enter a value or expression for each
variable, and then press Í. The values are stored, and the program
resumes execution.
Prompt variableA[,variableB,...,variable n]
Program
Output
Note: Y= functions are not valid with Prompt.
Displaying the Home Screen
Disp (display) without a value displays the home screen. To view the
home screen during program execution, follow the Disp instruction with a
Pause instruction.
Disp
TI-83 Plus
Programming
528
Displaying Values and Messages
Disp with one or more values displays the value of each.
Disp [valueA,valueB,valueC,...,value n]
• If value is a variable, the current value is displayed.
• If value is an expression, it is evaluated and the result is displayed on
the right side of the next line.
• If value is text within quotation marks, it is displayed on the left side of
the current display line. ! is not valid as text.
Program
Output
If Pause is encountered after Disp, the program halts temporarily so you
can examine the screen. To resume execution, press Í.
Note: If a matrix or list is too large to display in its entirety, ellipses (...) are
displayed in the last column, but the matrix or list cannot be scrolled. To scroll,
use Pause value.
TI-83 Plus
Programming
529
DispGraph
DispGraph (display graph) displays the current graph. If Pause is
encountered after DispGraph, the program halts temporarily so you can
examine the screen. Press Í to resume execution.
DispTable
DispTable (display table) displays the current table. The program halts
temporarily so you can examine the screen. Press Í to resume
execution.
Output(
Output( displays text or value on the current home screen beginning at row
(1 through 8) and column (1 through 16), overwriting any existing
characters.
Tip: You may want to precede Output( with ClrHome.
Expressions are evaluated and values are displayed according to the
current mode settings. Matrices are displayed in entry format and wrap
to the next line. ! is not valid as text.
Output(row,column,"text")
Output(row,column,value)
TI-83 Plus
Programming
530
Program
Output
For Output( on a Horiz split screen, the maximum value for row is 4.
getKey
getKey returns a number corresponding to the last key pressed,
according to the key code diagram below. If no key has been pressed,
getKey returns 0. Use getKey inside loops to transfer control, for
example, when creating video games.
Program
Output
Note: , Œ, , and
Í were pressed during
program execution.
Note: You can press É at any time during execution to break the program.
TI-83 Plus
Programming
531
GetCalc(
GetCalc( gets the contents of variable on another TI-83 Plus and stores it
to variable on the receiving TI-83 Plus. variable can be a real or complex
number, list element, list name, matrix element, matrix name, string,
Y= variable, graph database, or picture.
GetCalc(variable)
Note: GetCalc( does not work between TI.82 and TI-83 Plus calculators.
Get(, Send(
Get( gets data from the CBL 2/CBL or CBR and stores it to variable on the
receiving TI-83 Plus. variable can be a real number, list element, list
name, matrix element, matrix name, string, Y= variable, graph database,
or picture.
Get(variable)
Note: If you transfer a program that references the Get( command to the
TI-83 Plus from a TI.82, the TI-83 Plus will interpret it as the Get( described
above. Use GetCalc( to get data from another TI-83 Plus.
Send( sends the contents of variable to the CBL 2/CBL or CBR. You
cannot use it to send to another TI-83 Plus. variable can be a real
number, list element, list name, matrix element, matrix name, string,
Y= variable, graph database, or picture. variable can be a list of elements.
TI-83 Plus
Programming
533
Send(variable)
Note: This program gets sound
data and time in seconds from
CBL 2/CBL.
Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute
them from the home screen (Chapter 15).
TI-83 Plus
Programming
534
Calling Other Programs as Subroutines
Calling a Program from Another Program
On the TI-83 Plus, any stored program can be called from another
program as a subroutine. Enter the name of the program to use as a
subroutine on a line by itself.
You can enter a program name on a command line in either of two ways.
• Press | to display the PRGM EXEC menu and select the name of
the program prgmname is pasted to the current cursor location on a
command line.
• Select prgm from the PRGM CTL menu, and then enter the program
name.
prgmname
When prgmname is encountered during execution, the next command that
the program executes is the first command in the second program. It
returns to the subsequent command in the first program when it
encounters either Return or the implied Return at the end of the second
program.
TI-83 Plus
Programming
535
Program
Output
&
Subroutine ( '
Notes about Calling Programs
Variables are global.
label used with Goto and Lbl is local to the program where it is located.
label in one program is not recognized by another program. You cannot
use Goto to branch to a label in another program.
Return exits a subroutine and returns to the calling program, even if it is
encountered within nested loops.
TI-83 Plus
Programming
536
Running an Assembly Language Program
You can run programs written for the TI-83 Plus in assembly language.
Typically, assembly language programs run much faster and provide
greater control than than the keystroke programs that you write with the
built-in program editor.
Note: Because an assembly langauge program has greater control over the
calculator, if your assembly language program has error(s), it may cause your
calculator to reset and lose all data, programs, and applications stored in
memory.
When you download an assembly language program, it is stored among
the other programs as a PRGM menu item. You can:
• Transmit it using the TI-83 Plus communication link (Chapter 19).
• Delete it using the MEM MGMT DEL screen (Chapter 18).
To run an assembly Program, the syntax is: Asm(assemblyprgmname)
If you write an assembly language program, use the two instructions below
from the CATALOG to identify and compile the program.
TI-83 Plus
Programming
537
Instructions
Comments
AsmComp(prgmASM1, Compiles an assembly language program written in
prgmASM2)
ASCII and stores the hex version
AsmPrgm
Identifies an assembly language program; must be
entered as the first line of an assembly language
program
To compile an assembly program that you have written:
1. Follow the steps for writing a program (16-4) but be sure to include
AsmPrgm as the first line of your program.
2. From the home screen, press y N and then select AsmComp(
to paste it to the screen
3. Press to display the PRGM EXEC menu.
4. Select the program you want to compile. It will be pasted to the home
screen.
5. Press ¢ and then select prgm from the CATALOG
6. Key in the name you have chosen for the output program.
Note: This name must be unique — not a copy of an existing program
name.
TI-83 Plus
Programming
538
7. Press ¤ to complete the sequence.
The sequence of the arguments should be as follows:
AsmComp(prgmASM1, prgmASM2)
8. Press Í to compile your program and generate the output
program.
TI-83 Plus
Programming
539
Chapter 17:
Activities
The Quadratic Formula
Entering a Calculation
2
Use the quadratic formula to solve the quadratic equations 3X + 5X + 2 = 0 and
2
2
2X N X + 3 = 0. Begin with the equation 3X + 5X + 2 = 0.
1. Press 3 ¿ ƒ [A] (above ) to store
the coefficient of the X2 term.
2. Press ƒ [ : ] (above Ë). The colon allows
you to enter more than one instruction on a line.
3. Press 5 ¿ ƒ [B] (above Œ) to store
the coefficient of the X term. Press ƒ [ : ] to
enter a new instruction on the same line. Press
2 ¿ ƒ [C] (above ) to store the
constant.
TI-83 Plus
Activities
540
4. Press Í to store the values to the variables
A, B, and C.
The last value you stored is shown on the right
side of the display. The cursor moves to the
next line, ready for your next entry.
5. Press £ Ì ƒ [B] Ã y C ƒ [B] ¡
¹ 4 ƒ [A] ƒ [C] ¤ ¤ ¥ £ 2 ƒ [A]
¤ to enter the expression for one of the
solutions for the quadratic formula,
−b± b2−4ac
2a
6. Press Í to find one solution for the
equation 3X2 + 5X + 2 = 0.
The answer is shown on the right side of the
display. The cursor moves to the next line,
ready for you to enter the next expression.
TI-83 Plus
Activities
541
The Quadratic Formula
Converting to a Fraction
You can show the solution as a fraction.
1. Press to display the MATH menu.
2. Press 1 to select 1:4Frac from the MATH menu.
When you press 1, Ans4Frac is displayed on the
home screen. Ans is a variable that contains the
last calculated answer.
3. Press Í to convert the result to a fraction.
TI-83 Plus
Activities
542
To save keystrokes, you can recall the last expression you entered, and
then edit it for a new calculation.
4. Press y [ (above Í) to recall the
fraction conversion entry, and then press y
[ again to recall the quadratic-formula
expression,
−b+ b2−4ac
2a
5. Press } to move the cursor onto the + sign in
the formula. Press ¹ to edit the quadratic-
formula expression to become:
−b− b2−4ac
2a
6. Press Í to find the other solution for the
quadratic equation 3X2 + 5X + 2 = 0.
TI-83 Plus
Activities
543
The Quadratic Formula
Displaying Complex Results
Now solve the equation 2X2 N X + 3 = 0. When you set a+bi complex
number mode, the TI-83 Plus displays complex results.
1. Press z † † † † † † (6 times), and
then press ~ to position the cursor over a+bi.
Press Í to select a+bi complex-number
mode.
2. Press y 5 (above z) to return to the
home screen, and then press ‘ to clear it.
3. Press 2 ¿ ƒ [A] ƒ [ : ] Ì 1 ¿
ƒ [B] ƒ [ : ] 3 ¿ ƒ [C] Í.
The coefficient of the X2 term, the coefficient of
the X term, and the constant for the new
equation are stored to A, B, and C, respectively.
TI-83 Plus
Activities
544
4. Press y [ to recall the store instruction,
and then press y [ again to recall the
quadratic-formula expression,
−b− b2−4ac
2a
5. Press Í to find one solution for the
equation 2X2 N X + 3 = 0.
6. Press y [ repeatedly until this quadratic-
formula expression is displayed:
−b+ b2−4ac
2a
7. Press Í to find the other solution for the
quadratic equation: 2X2 N X + 3 = 0.
Note: An alternative for solving equations for real numbers is to use the built-in
Equation Solver (Chapter 2).
TI-83 Plus
Activities
545
Box with Lid
Defining a Function
Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two
corners. Cut X × 12.5 cm rectangles from the other two corners as
shown in the diagram below. Fold the paper into a box with a lid. What
value of X would give your box the maximum volume V? Use the table
and graphs to determine the solution.
Begin by defining a function that describes the
volume of the box.
X
20 A
From the diagram: 2X + A = 20
2X + 2B = 25
X B
X B
25
V = A*B*X
Substituting: V = (20 N 2X) (25à2 N X) X
1. Press o to display the Y= editor, which is
where you define functions for tables and
graphing.
TI-83 Plus
Activities
546
2. Press £ 20 ¹ 2 „ ¤ £ 25 ¥ 2 ¹ „
¤ „ Í to define the volume function
as Y1 in terms of X.
„ lets you enter X quickly, without having
to press ƒ. The highlighted = sign indicates
that Y1 is selected.
Box with Lid
Defining a Table of Values
The table feature of the TI-83 Plus displays numeric information about a
function. You can use a table of values from the function you just defined
to estimate an answer to the problem.
1. Press y - (above p) to display the
TABLE SETUP menu.
2. Press Í to accept TblStart=0.
3. Press 1 Í to define the table increment
@Tbl=1. Leave Indpnt: Auto and Depend: Auto so
that the table will be generated automatically.
TI-83 Plus
Activities
547
4. Press y 0 (above s) to display the
table.
Notice that the maximum value for Y1 (box’s
volume) occurs when X is about 4, between 3
and 5.
5. Press and hold † to scroll the table until a
negative result for Y1 is displayed.
Notice that the maximum length of X for this
problem occurs where the sign of Y1 (box’s
volume) changes from positive to negative,
between 10 and 11.
6. Press y -.
Notice that TblStart has changed to 6 to reflect
the first line of the table as it was last displayed.
(In step 5, the first value of X displayed in the
table is 6.)
TI-83 Plus
Activities
548
Box with Lid
Zooming In on the Table
You can adjust the way a table is displayed to get more information
about a defined function. With smaller values for @Tbl, you can zoom in
on the table.
1. Press 3 Í to set TblStart. Press Ë 1 Í
to set @Tbl.
This adjusts the table setup to get a more
accurate estimate of X for maximum volume Y1.
2. Press y 0.
3. Press † and } to scroll the table.
Notice that the maximum value for Y1 is 410.26,
which occurs at X=3.7. Therefore, the maximum
occurs where 3.6<X<3.8.
TI-83 Plus
Activities
549
4. Press y -. Press 3 Ë 6 Í to set
TblStart. Press Ë 01 Í to set @Tbl.
5. Press y 0, and then press † and } to
scroll the table.
Four equivalent maximum values are shown,
410.26 at X=3.67, 3.68, 3.69, and 3.70.
6. Press † or } to move the cursor to 3.67. Press
~ to move the cursor into the Y1 column.
The value of Y1 at X=3.67 is displayed on the
bottom line in full precision as 410.261226.
TI-83 Plus
Activities
550
7. Press † to display the other maximum.
The value of Y1 at X=3.68 in full precision is
410.264064, at X=3.69 is 410.262318 and at X=3.7
is 410.256.
The maximum volume of the box would occur at
3.68 if you could measure and cut the paper at
.01-centimeter increments.
Box with Lid
Setting the Viewing Window
You also can use the graphing features of the TI-83 Plus to find the
maximum value of a previously defined function. When the graph is
activated, the viewing window defines the displayed portion of the
coordinate plane. The values of the window variables determine the size
of the viewing window.
1. Press p to display the window editor,
where you can view and edit the values of the
window variables.
TI-83 Plus
Activities
551
Ymax
Xscl
The standard window variables define the
viewing window as shown. Xmin, Xmax, Ymin,
and Ymax define the boundaries of the display.
Xscl and Yscl define the distance between tick
marks on the X and Y axes. Xres controls
resolution.
Xmin
Xmax
Yscl
Ymin
2. Press 0 Í to define Xmin.
3. Press 20 ¥ 2 to define Xmax using an
expression.
4. Press Í. The expression is evaluated, and
10 is stored in Xmax. Press Í to accept Xscl
as 1.
5. Press 0 Í 500 Í 100 Í 1 Í to
define the remaining window variables.
TI-83 Plus
Activities
552
Box with Lid
Displaying and Tracing the Graph
Now that you have defined the function to be graphed and the window in
which to graph it, you can display and explore the graph. You can trace
along a function using the TRACE feature.
1. Press s to graph the selected function in
the viewing window.
The graph of Y1=(20N2X)(25à2NX)X is displayed.
2. Press ~ to activate the free-moving graph
cursor.
The X and Y coordinate values for the position
of the graph cursor are displayed on the bottom
line.
TI-83 Plus
Activities
553
3. Press |, ~, }, and † to move the free-
moving cursor to the apparent maximum of the
function.
As you move the cursor, the X and Y coordinate
values are updated continually.
4. Press r. The trace cursor is displayed on
the Y1 function.
The function that you are tracing is displayed in
the top-left corner.
5. Press | and ~ to trace along Y1, one X dot at
a time, evaluating Y1 at each X.
You also can enter your estimate for the
maximum value of X.
6. Press 3 Ë 8. When you press a number key
while in TRACE, the X= prompt is displayed in the
bottom-left corner.
TI-83 Plus
Activities
554
7. Press Í.
The trace cursor jumps to the point on the Y1
function evaluated at X=3.8.
8. Press | and ~ until you are on the maximum
Y value.
This is the maximum of Y1(X) for the X pixel
values. The actual, precise maximum may lie
between pixel values.
Box with Lid
Zooming In on the Graph
To help identify maximums, minimums, roots, and intersections of
functions, you can magnify the viewing window at a specific location
using the ZOOM instructions.
TI-83 Plus
Activities
555
1. Press q to display the ZOOM menu.
This menu is a typical TI-83 Plus menu. To
select an item, you can either press the number
or letter next to the item, or you can press †
until the item number or letter is highlighted,
and then press Í.
2. Press 2 to select 2:Zoom In.
The graph is displayed again. The cursor has
changed to indicate that you are using a ZOOM
instruction.
3. With the cursor near the maximum value of the
function, press Í.
The new viewing window is displayed. Both
XmaxNXmin and YmaxNYmin have been
adjusted by factors of 4, the default values for
the zoom factors.
TI-83 Plus
Activities
556
4. Press p to display the new window
settings.
Box with Lid
Finding the Calculated Maximum
You can use a CALCULATE menu operation to calculate a local maximum
of a function.
1. Press y / (above r) to display the
CALCULATE menu. Press 4 to select 4:maximum.
The graph is displayed again with a Left Bound?
prompt.
TI-83 Plus
Activities
557
2. Press | to trace along the curve to a point to
the left of the maximum, and then press Í.
A 4 at the top of the screen indicates the
selected bound.
A Right Bound? prompt is displayed.
3. Press ~ to trace along the curve to a point to
the right of the maximum, and then press
Í.
A 3 at the top of the screen indicates the
selected bound.
A Guess? prompt is displayed.
4. Press | to trace to a point near the maximum,
and then press Í.
TI-83 Plus
Activities
558
Or, press 3 Ë 8, and then press Í to enter
a guess for the maximum.
When you press a number key in TRACE, the X=
prompt is displayed in the bottom-left corner.
Notice how the values for the calculated
maximum compare with the maximums found
with the free-moving cursor, the trace cursor,
and the table.
Note: In steps 2 and 3 above, you can enter values
directly for Left Bound and Right Bound, in the same
way as described in step 4.
TI-83 Plus
Activities
559
Comparing Test Results Using Box Plots
Problem
An experiment found a significant difference between boys and girls
pertaining to their ability to identify objects held in their left hands, which
are controlled by the right side of their brains, versus their right hands,
which are controlled by the left side of their brains. The TI Graphics team
conducted a similar test for adult men and women.
The test involved 30 small objects, which participants were not allowed to
see. First, they held 15 of the objects one by one in their left hands and
guessed what they were. Then they held the other 15 objects one by one
in their right hands and guessed what they were. Use box plots to
compare visually the correct-guess data from this table.
Correct Guesses
Women
Left
Women
Right
Men
Left
Men
Right
8
9
12
11
10
8
4
1
8
12
11
11
7
8
7
5
7
8
12
6
12
12
7
11
TI-83 Plus
Activities
560
Women
Left
Women
Right
Men
Left
Men
Right
12
7
9
13
12
11
12
11
4
10
14
13
5
12
8
12
11
9
11
9
Procedure
1. Press … 5 to select 5:SetUpEditor. Enter list names WLEFT,
WRGHT, MLEFT, and MRGHT, separated by commas. Press Í.
The stat list editor now contains only these four lists.
2. Press … 1 to select 1:Edit.
3. Enter into WLEFT the number of correct guesses each woman made
using her left hand (Women Left). Press ~ to move to WRGHT and enter
the number of correct guesses each woman made using her right hand
(Women Right).
4. Likewise, enter each man’s correct guesses in MLEFT (Men Left) and
MRGHT (Men Right).
TI-83 Plus
Activities
561
5. Press y ,. Select 1:Plot1. Turn on plot 1; define it as a
modified box plot Õ that uses WLEFT. Move the cursor to the top line
and select Plot2. Turn on plot 2; define it as a modified box plot that
uses WRGHT.
6. Press o. Turn off all functions.
7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select
9:ZoomStat. This adjusts the viewing window and displays the box
plots for the women’s results.
8. Press r.
% Women’s left-hand data
% Women’s right-hand data
Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot.
Notice the outlier to the women’s right-hand data. What is the median
for the left hand? For the right hand? With which hand were the
women more accurate guessers, according to the box plots?
9. Examine the men’s results. Redefine plot 1 to use MLEFT, redefine
plot 2 to use MRGHT. Press r.
TI-83 Plus
Activities
562
% Men’s left-hand data
% Men’s right-hand data
Press | and ~ to examine minX, Q1, Med, Q3, and maxX for each
plot. What difference do you see between the plots?
10.Compare the left-hand results. Redefine plot 1 to use WLEFT,
redefine plot 2 to use MLEFT, and then press r to examine minX,
Q1, Med, Q3, and maxX for each plot. Who were the better left-hand
guessers, men or women?
11.Compare the right-hand results. Define plot 1 to use WRGHT, define plot
2 to use MRGHT, and then press r to examine minX, Q1, Med, Q3,
and maxX for each plot. Who were the better right-hand guessers?
In the original experiment boys did not guess as well with right hands,
while girls guessed equally well with either hand. This is not what our
box plots show for adults. Do you think that this is because adults
have learned to adapt or because our sample was not large enough?
TI-83 Plus
Activities
563
Graphing Piecewise Functions
Problem
The fine for speeding on a road with a speed limit of 45 kilometers per
hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each
kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above.
Graph the piecewise function that describes the cost of the ticket.
The fine (Y) as a function of kilometers per hour (X) is:
Y = 0
Y = 50 + 5 (X N 45)
Y = 50 + 5 ä 10 + 10 (X N 55)
Y = 50 + 5 ä 10 + 10 ä 10 + 20 (X N 65)
0 < X 45
45 < X 55
55 < X 65
65 < X
Procedure
1. Press z. Select Func and the default settings.
2. Press o. Turn off all functions and stat plots. Enter the Y= function to
describe the fine. Use the TEST menu operations to define the
piecewise function. Set the graph style for Y1 to í (dot).
TI-83 Plus
Activities
564
3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10. Ignore
Xmax and Ymax; they are set by @X and @Y in step 4.
4. Press y 5 to return to the home screen. Store 1 to @X, and then
store 5 to @Y. @X and @Y are on the VARS Window X/Y secondary menu.
@X and @Y specify the horizontal and vertical distance between the
centers of adjacent pixels. Integer values for @X and @Y produce nice
values for tracing.
5. Press r to plot the function. At what speed does the ticket
exceed 250?
TI-83 Plus
Activities
565
Graphing Inequalities
Problem
Graph the inequality 0.4X3 N 3X + 5 < 0.2X + 4. Use the TEST menu
operations to explore the values of X where the inequality is true and
where it is false.
Procedure
1. Press z. Select Dot, Simul, and the default settings. Setting Dot
mode changes all graph style icons to í (dot) in the Y= editor.
2. Press o. Turn off all functions and stat plots. Enter the left side of the
inequality as Y4 and the right side as Y5.
3. Enter the statement of the inequality as Y6. This function evaluates to
1 if true or 0 if false.
TI-83 Plus
Activities
566
4. Press q 6 to graph the inequality in the standard window.
5. Press r † † to move to Y6. Then press | and ~ to trace the
inequality, observing the value of Y.
6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the
inequality.
7. Press r. Notice that the values of Y7 and Y8 are zero where the
inequality is false.
TI-83 Plus
Activities
567
Solving a System of Nonlinear Equations
Problem
Using a graph, solve the equation X3 N 2X = 2cos(X). Stated another
way, solve the system of two equations and two unknowns: Y = X3N2X
and Y = 2cos(X). Use ZOOM factors to control the decimal places
displayed on the graph.
Procedure
1. Press z. Select the default mode settings. Press o. Turn off all
functions and stat plots. Enter the functions.
2. Press q 4 to select 4:ZDecimal. The display shows that two
solutions may exist (points where the two functions appear to
intersect).
TI-83 Plus
Activities
568
3. Press q ~ 4 to select 4:SetFactors from the ZOOM MEMORY menu.
Set XFact=10 and YFact=10.
4. Press q 2 to select 2:Zoom In. Use |, ~, }, and † to move the
free-moving cursor onto the apparent intersection of the functions on
the right side of the display. As you move the cursor, notice that the X
and Y values have one decimal place.
5. Press Í to zoom in. Move the cursor over the intersection. As
you move the cursor, notice that now the X and Y values have two
decimal places.
6. Press Í to zoom in again. Move the free-moving cursor onto a
point exactly on the intersection. Notice the number of decimal
places.
7. Press y / 5 to select 5:intersect. Press Í to select the first
curve and Í to select the second curve. To guess, move the
trace cursor near the intersection. Press Í. What are the
coordinates of the intersection point?
8. Press q 4 to select 4:ZDecimal to redisplay the original graph.
9. Press q. Select 2:Zoom In and repeat steps 4 through 8 to explore
the apparent function intersection on the left side of the display.
TI-83 Plus
Activities
569
Using a Program to Create the Sierpinski
Triangle
Setting up the Program
This program creates a drawing of a famous fractal, the Sierpinski
Triangle, and stores the drawing to a picture. To begin, press ~ ~
1. Name the program SIERPINS, and then press Í. The program
editor is displayed.
Program
PROGRAM:SIERPINS
:FnOff :ClrDraw
:PlotsOff
:AxesOff
:0!Xmin:1!Xmax
:0!Ymin:1!Ymax
Set viewing window.
:rand!X:rand!Y
:For(K,1,3000)
:rand!N
Beginning of For group.
:If N1à3
:Then
If/Then group
:.5X!X
:.5Y!Y
:End
TI-83 Plus
Activities
570
:If 1à3<N and N2à3
:Then
:.5(.5+X)!X
:.5(1+Y)!Y
:End
If/Then group.
:If 2à3<N
:Then
:.5(1+X)!X
:.5Y!Y
If/Then group.
:End
:Pt-On(X,Y)
Draw point.
:End
End of For group.
Store picture.
:StorePic 6
After you execute the program above, you can recall and display the
picture with the instruction RecallPic 6.
TI-83 Plus
Activities
571
Graphing Cobweb Attractors
Problem
Using Web format, you can identify points with attracting and repelling
behavior in sequence graphing.
Procedure
1. Press z. Select Seq and the default mode settings. Press y
.. Select Web format and the default format settings.
2. Press o. Clear all functions and turn off all stat plots. Enter the
sequence that corresponds to the expression Y = K X(1NX).
u(n)=Ku(nN1)(1Nu(nN1))
u(nMin)=.01
3. Press y 5 to return to the home screen, and then store 2.9 to K.
4. Press p. Set the window variables.
nMin=0
Xmin=0
Xmax=1
Xscl=1
Ymin=M.26
Ymax=1.1
Yscl=1
nMax=10
PlotStart=1
PlotStep=1
TI-83 Plus
Activities
572
5. Press r to display the graph, and then press ~ to trace the
cobweb. This is a cobweb with one attractor.
6. Change K to 3.44 and trace the graph to show a cobweb with two
attractors.
7. Change K to 3.54 and trace the graph to show a cobweb with four
attractors.
TI-83 Plus
Activities
573
Using a Program to Guess the Coefficients
Setting Up the Program
This program graphs the function A sin(BX) with random integer
coefficients between 1 and 10. Try to guess the coefficients and graph
your guess as C sin(DX). The program continues until your guess is
correct.
Program
PROGRAM:GUESS
:PlotsOff :Func
:FnOff :Radian
:ClrHome
:"Asin(BX)"!Y1
Define equations.
:"Csin(DX)"!Y2
:GraphStyle(1,1)
Set line and path graph styles.
:GraphStyle(2,5)
:FnOff 2
:randInt(1,10)!A
:randInt(1,10)!B
:0!C:0!D
:L2p!Xmin
Initialize coefficients.
Set viewing window.
:2p!Xmax
:pà2!Xscl
:L10!Ymin
:10!Ymax
TI-83 Plus
Activities
574
:1!Yscl
:DispGraph
:Pause
Display graph.
:FnOn 2
:Lbl Z
:Prompt C,D
Prompt for guess.
Display graph.
:DispGraph
:Pause
:If C=A
:Text(1,1,"C IS OK")
:If CƒA
:Text(1,1,"C IS WRONG")
:If D=B
Display results.
:Text(1,50,"D IS OK")
:If DƒB
:Text(1,50,"D IS WRONG")
:DispGraph
:Pause
Display graph.
:If C=A and D=B
:Stop
:Goto Z
Quit if guesses are correct.
TI-83 Plus
Activities
575
Graphing the Unit Circle and Trigonometric
Curves
Problem
Using parametric graphing mode, graph the unit circle and the sine curve
to show the relationship between them.
Any function that can be plotted in Func mode can be plotted in Par mode
by defining the X component as T and the Y component as F(T).
Procedure
1. Press z. Select Par, Simul, and the default settings.
2. Press p. Set the viewing window.
Tmin=0
Tmax=2p
Tstep=.1
Xmin=L2
Xmax=7.4
Xscl=pà2
Ymin=L3
Ymax=3
Yscl=1
3. Press o. Turn off all functions and stat plots. Enter the expressions
to define the unit circle centered on (0,0).
TI-83 Plus
Activities
576
4. Enter the expressions to define the sine curve.
5. Press r. As the graph is plotting, you may press Í to pause
and Í again to resume graphing as you watch the sine function
“unwrap” from the unit circle.
Note: You can generalize the unwrapping. Replace sin(T) in Y2T with any other
trig function to unwrap that function.
TI-83 Plus
Activities
577
Finding the Area between Curves
Problem
Find the area of the region bounded by
f(x) = 300x/(x2 + 625)
g(x)= 3cos(.1x)
x
= 75
Procedure
1. Press z. Select the default mode settings.
2. Press p. Set the viewing window.
Xmin=0
Xmax=100
Xscl=10
Ymin=L5
Ymax=10
Yscl=1
Xres=1
3. Press o. Turn off all functions and stat plots. Enter the upper and
lower functions.
2
Y1=300Xà(X +625)
Y2=3cos(.1X)
TI-83 Plus
Activities
578
4. Press y / 5 to select 5:Intersect. The graph is displayed. Select
a first curve, second curve, and guess for the intersection toward the
left side of the display. The solution is displayed, and the value of X at
the intersection, which is the lower limit of the integral, is stored in
Ans and X.
5. Press y 5 to go to the home screen. Press y < 7 and use
Shade( to see the area graphically.
Shade(Y2,Y1,Ans,75)
6. Press y 5 to return to the home screen. Enter the expression to
evaluate the integral for the shaded region.
fnInt(Y1–Y2,X,Ans,75)
The area is 325.839962.
TI-83 Plus
Activities
579
Using Parametric Equations: Ferris Wheel
Problem
Problem
Using two pairs of parametric equations, determine when two objects in
motion are closest to each other in the same plane.
A ferris wheel has a diameter (d) of 20 meters and is rotating
counterclockwise at a rate (s) of one revolution every 12 seconds. The
parametric equations below describe the location of a ferris wheel
passenger at time T, where a is the angle of rotation, (0,0) is the bottom
center of the ferris wheel, and (10,10) is the passenger’s location at the
rightmost point, when T=0.
X(T) = r cos a
where a = 2pTs and r = dà2
Y(T) = r + r sin a
A person standing on the ground throws a ball to the ferris wheel
passenger. The thrower’s arm is at the same height as the bottom of the
ferris wheel, but 25 meters (b) to the right of the ferris wheel’s lowest point
(25,0). The person throws the ball with velocity (v0) of 22 meters per
second at an angle (q) of 66¡ from the horizontal. The parametric
equations below describe the location of the ball at time T.
X(T) = b N Tv0 cosq
Y(T) = Tv0 sinq N (gà2) T2
where g = 9.8 m/sec2
TI-83 Plus
Activities
580
Procedure
1. Press z. Select Par, Simul, and the default settings. Simul
(simultaneous) mode simulates the two objects in motion over time.
2. Press p. Set the viewing window.
Tmin=0
Tmax=12
Tstep=.1
Xmin=L13
Xmax=34
Xscl=10
Ymin=0
Ymax=31
Yscl=10
3. Press o. Turn off all functions and stat plots. Enter the expressions to
define the path of the ferris wheel and the path of the ball. Set the
graph style for X2T to ë (path).
Tip: Try setting the graph styles to ë X1T and ì X2T, which simulates a chair on
the ferris wheel and the ball flying through the air when you press s.
TI-83 Plus
Activities
581
4. Press s to graph the equations. Watch closely as they are
plotted. Notice that the ball and the ferris wheel passenger appear to
be closest where the paths cross in the top-right quadrant of the ferris
wheel.
5. Press p. Change the viewing window to concentrate on this
portion of the graph.
Tmin=1
Tmax=3
Tstep=.03
Xmin=0
Xmax=23.5
Xscl=10
Ymin=10
Ymax=25.5
Yscl=10
6. Press r. After the graph is plotted, press ~ to move near the
point on the ferris wheel where the paths cross. Notice the values of
X, Y, and T.
TI-83 Plus
Activities
582
7. Press † to move to the path of the ball. Notice the values of X and Y
(T is unchanged). Notice where the cursor is located. This is the
position of the ball when the ferris wheel passenger passes the
intersection. Did the ball or the passenger reach the intersection first?
You can use r to, in effect, take snapshots in time and explore
the relative behavior of two objects in motion.
TI-83 Plus
Activities
583
Demonstrating the Fundamental Theorem of
Calculus
Problem 1
Using the functions fnInt( and nDeriv( from the MATH menu to graph
functions defined by integrals and derivatives demonstrates graphically
that:
x
F(x) = dt = ln(x), x > 0 and that
∫
1
x
Dx
1 dt = 1
∫
x
t
1
Procedure 1
1. Press z. Select the default settings.
2. Press p. Set the viewing window.
Xmin=.01
Xmax=10
Xscl=1
Ymin=M1.5
Ymax=2.5
Yscl=1
Xres=3
TI-83 Plus
Activities
584
3. Press o. Turn off all functions and stat plots. Enter the numerical
integral of 1àT from 1 to X and the function ln(X). Set the graph style
for Y1 to ç (line) and Y2 to ë (path).
4. Press r. Press |, }, ~, and † to compare the values of Y1
and Y2.
5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative
of the integral of 1àX and the function 1àX. Set the graph style for Y3
to ç (line) and Y4 to è (thick).
6. Press r. Again, use the cursor keys to compare the values of the
two graphed functions, Y3 and Y4.
TI-83 Plus
Activities
585
Problem 2
Explore the functions defined by
x
x
x
y = t2dt,
t2dt, and
t2dt,
∫
2
∫
0
∫
2
Procedure 2
1. Press o. Turn off all functions and stat plots. Use a list to define
these three functions simultaneously. Store the function in Y5.
2. Press q 6 to select 6:ZStandard.
3. Press r. Notice that the functions appear identical, only shifted
vertically by a constant.
TI-83 Plus
Activities
586
4. Press o. Enter the numerical derivative of Y5 in Y6.
5. Press r. Notice that although the three graphs defined by Y5 are
different, they share the same derivative.
TI-83 Plus
Activities
587
Computing Areas of Regular N-Sided
Polygons
Problem
Use the equation solver to store a formula for the area of a regular
N-sided polygon, and then solve for each variable, given the other
variables. Explore the fact that the limiting case is the area of a circle,
pr2.
Consider the formula A = NB2 sin(pàN) cos(pàN) for the area of a
regular polygon with N sides of equal length and B distance from the
center to a vertex.
N = 4 sides
N = 8 sides
N = 12 sides
Procedure
1. Press 0 to select 0:Solver from the MATH menu. Either the
equation editor or the interactive solver editor is displayed. If the
TI-83 Plus
Activities
588
interactive solver editor is displayed, press } to display the equation
editor.
2. Enter the formula as 0=ANNB2sin(p / N)cos(p / N), and then press
Í. The interactive solver editor is displayed.
3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B)
from center to vertex of 6 centimeters.
4. Press } } to move the cursor onto A, and then press ƒ \.
The solution for A is displayed on the interactive solver editor.
5. Now solve for B for a given area with various number of sides. Enter
A=200 and N=6. To find the distance B, move the cursor onto B, and
then press ƒ \.
TI-83 Plus
Activities
589
6. Enter N=8. To find the distance B, move the cursor onto B, and then
press ƒ \. Find B for N=9, and then for N=10.
Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare
your results with p62 (the area of a circle with radius 6), which is
approximately 113.097.
7. Enter B=6. To find the area A, move the cursor onto A, and then press
ƒ \. Find A for N=10, then N=100, then N=150, then N=1000,
and finally N=10000. Notice that as N gets large, the area A
approaches pB2.
Now graph the equation to see visually how the area changes as the
number of sides gets large.
8. Press z. Select the default mode settings.
9. Press p. Set the viewing window.
Xmin=0
Ymin=0
Xres=1
Xmax=200
Xscl=10
Ymax=150
Yscl=10
10.Press o. Turn off all functions and stat plots. Enter the equation for
the area. Use X in place of N. Set the graph styles as shown.
TI-83 Plus
Activities
590
11.Press r. After the graph is plotted, press 100 Í to trace to
X=100. Press 150 Í. Press 188 Í. Notice that as X increases,
the value of Y converges to p62, which is approximately 113.097.
Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The
area of an N-sided regular polygon, with r as the distance from the
center to a vertex, approaches the area of a circle with radius r (pr2)
as N gets large.
TI-83 Plus
Activities
591
Computing and Graphing Mortgage
Payments
Problem
You are a loan officer at a mortgage company, and you recently closed
on a 30-year home mortgage at 8 percent interest with monthly
payments of 800. The new home owners want to know how much will be
applied to the interest and how much will be applied to the principal
when they make the 240th payment 20 years from now.
Procedure
1. Press z and set the fixed-decimal mode to 2 decimal places. Set
the other mode settings to the defaults.
2. Press Œ Í Í to display the TVM Solver. Enter these values.
Note: Enter a positive number (800) to show PMT as a cash inflow. Payment
values will be displayed as positive numbers on the graph. Enter 0 for FV,
TI-83 Plus
Activities
592
since the future value of a loan is 0 once it is paid in full. Enter PMT: END,
since payment is due at the end of a period.
3. Move the cursor onto the PV= prompt, and then press ƒ \.
The present value, or mortgage amount, of the house is displayed at
the PV= prompt.
Now compare the graph of the amount of interest with the graph of the
amount of principal for each payment.
4. Press z. Set Par and Simul.
5. Press o. Turn off all functions and stat plots. Enter these equations
and set the graph styles as shown.
Note: GPrn( and GInt( are located on the FINANCE menu (APPS 1:FINANCE).
TI-83 Plus
Activities
593
6. Press p. Set these window variables.
Tmin=1
Xmin=0
Ymin=0
Tmax=360
Tstep=12
Xmax=360
Xscl=10
Ymax=1000
Yscl=100
Tip: To increase the graph speed, change Tstep to 24.
7. Press r. After the graph is drawn, press 240 Í to move the
trace cursor to T=240, which is equivalent to 20 years of payments.
The graph shows that for the 240th payment (X=240), 358.03 of the
800 payment is applied to principal (Y=358.03).
Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800.
8. Press † to move the cursor onto the function for interest defined by
X2T and Y2T. Enter 240.
TI-83 Plus
Activities
594
The graph shows that for the 240th payment (X=240), 441.97 of the
800 payment is interest (Y=441.97).
9. Press y 5 Œ Í 9 to paste 9:bal( to the home screen.
Check the figures from the graph.
At which monthly payment will the principal allocation surpass the
interest allocation?
TI-83 Plus
Activities
595
Chapter 18:
Memory and Variable Management
Checking Available Memory
MEMORY Menu
At any time you can check available memory or manage existing
memory by selecting items from the MEMORY menu. To access this menu,
press y L.
MEMORY
1:About...
Displays information about the calculator.
Reports memory availability and variable usage.
Clears ENTRY (last-entry storage).
Clears all lists in memory.
Archives a selected variable.
UnArchives a selected variable.
2:Mem Mgmt/Del...
3:Clear Entries
4:ClrAllLists
5:Archive...
6:UnArchive...
7:Reset...
Displays the RAM, ARCHIVE, and ALL menus
Displays GROUP and UNGROUP menus.
8:Group...
To check memory usage, first press y L and then press 2:Mem
Mgmt/Del.
TI-83 Plus
Memory and Variable Management
596
Displaying the MEMORY MANAGEMENT/DELETE Menu
Mem Mgmt/Del displays the MEMORY MANAGEMENT/DELETE menu. The two
lines at the top report the total amount of available RAM and ARCHIVE
memory. By selecting menu items on this screen, you can see the
amount of memory each variable type is using. This information can help
you determine if some variables need to be deleted from memory to
make room for new data, such as programs or applications.
To check memory usage, follow these steps.
1. Press y L to display the MEMORY menu.
Note: The # and $ in the top or bottom
of the left column indicate that you can
scroll up or down to view more
variable types.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE
menu. The TI-83 Plus expresses memory quantities in bytes.
TI-83 Plus
Memory and Variable Management
597
3. Select variable types from the list to display memory usage.
Note: Real, List, Y.Vars, and Prgm variable types never reset to zero, even
after memory is cleared.
Apps are independent applications which are stored in Flash ROM.
AppVars is a variable holder used to store variables created by independent
applications. You cannot edit or change variables in AppVars unless you do
so through the application which created them.
To leave the MEMORY MANAGEMENT/DELETE menu, press either
y 5 or ‘. Both options display the home screen.
TI-83 Plus
Memory and Variable Management
598
Deleting Items from Memory
Deleting an Item
To increase available memory by deleting the contents of any variable
(real or complex number, list, matrix, Y= variable, program, Apps,
AppVars, picture, graph database, or string), follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE
menu.
3. Select the type of data you want to delete, or select 1:All for a list of
all variables of all types. A screen is displayed listing each variable of
the type you selected and the number of bytes each variable is using.
For example, if you select 4:List, the LIST editor screen is displayed.
TI-83 Plus
Memory and Variable Management
599
4. Press } and † to move the selection cursor (4) next to the item you
want to delete, and then press {. The variable is deleted from
memory. You can delete individual variables one by one from this
screen.
Note: If you are deleting programs or Apps, you will receive a message
asking you to confirm this delete action. Select 2:Yes to continue.
To leave any variable screen without deleting anything, press
y 5, which displays the home screen.
Note: You cannot delete some system variables, such as the last-answer
variable Ans and the statistical variable RegEQ.
TI-83 Plus
Memory and Variable Management
600
Clearing Entries and List Elements
Clear Entries
Clear Entries clears the contents of the ENTRY (last entry) storage area
(Chapter 1). To clear the ENTRY storage area, follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 3:Clear Entries to paste the instruction to the home screen.
3. Press Í to clear the ENTRY storage area.
To cancel Clear Entries, press ‘.
Note: If you select 3:Clear Entries from within a program, the Clear Entries
instruction is pasted to the program editor, and the Entry (last entry) is cleared
when the program is executed.
TI-83 Plus
Memory and Variable Management
601
ClrAllLists
ClrAllLists sets the dimension of each list in RAM only to 0.
To clear all elements from all lists, follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 4:ClrAllLists to paste the instruction to the home screen.
3. Press Í to set to 0 the dimension of each list in memory.
To cancel ClrAllLists, press ‘.
ClrAllLists does not delete list names from memory, from the LIST NAMES
menu, or from the stat list editor.
Note: If you select 4:ClrAllLists from within a program, the ClrAllLists instruction
is pasted to the program editor. The lists are cleared when the program is
executed.
TI-83 Plus
Memory and Variable Management
602
Resetting the TI-83 Plus
RAM ARCHIVE ALL Menu
The RAM ARCHIVE ALL menu gives you the option of resetting all
memory (including default settings) or resetting selected portions of
memory while preserving other data stored in memory, such as
programs and Y= functions. For instance, you can choose to reset all of
RAM or just restore the default settings. Be aware that if you choose to
reset RAM, all data and programs in RAM will be erased. For archive
memory, you can reset variables (Vars), applications (Apps), or both of
these. Be aware that if you choose to reset Vars, all data and programs
in archive memory will be erased. If you choose to reset Apps, all
applications in archive memory will be erased.
When you reset defaults on the TI-83 Plus, all defaults in RAM are
restored to the factory settings. Stored data and programs are not
changed.
These are some examples of TI-83 Plus defaults that are restored by
resetting the defaults.
• Mode settings such as Normal (notation); Func (graphing); Real
(numbers); and Full (screen)
•
Y= functions off
TI-83 Plus
Memory and Variable Management
603
• Window variable values such as Xmin=L10; Xmax=10; Xscl=1; Yscl=1;
and Xres=1
• Stat plots off
• Format settings such as CoordOn (graphing coordinates on); AxesOn;
and ExprOn (expression on)
•
rand seed value to 0
Displaying the RAM ARCHIVE ALL Menu
To display the RAM ARCHIVE ALL menu on the TI-83 Plus, follow these
steps.
1. Press y L to display the MEMORY menu.
2. Select 7:Reset to display the RAM ARCHIVE ALL menu.
Resetting RAM Memory
Resetting RAM restores RAM system variables to factory settings and
deletes all nonsystem variables and all programs. Resetting defaults
restores all system variables to default settings without deleting variables
TI-83 Plus
Memory and Variable Management
604
and programs in RAM. Resetting RAM or resetting defaults does not
affect variables and applications in user data archive.
Tip: Before you reset all RAM memory, consider restoring sufficient available
memory by deleting only selected data.
To reset all RAM memory or RAM defaults on the TI-83 Plus, follow these
steps.
1. From the RAM ARCHIVE ALL menu, select 1:ALL RAM to display the
RESET RAM menu or 2:Defaults to display the RESET DEFAULTS menu.
2. If you are resetting RAM, read the message below the RESET RAM
menu.
• To cancel the reset and return to the home screen, press Í.
• To erase RAM memory or reset defaults, select 2:Reset.
Depending on your choice, the message RAM cleared or Defaults
set is displayed on the home screen.
TI-83 Plus
Memory and Variable Management
605
Resetting Archive Memory
When resetting archive memory on the TI-83 Plus, you can choose to
delete from user data archive all variables, all applications, or both
variables and applications.
To reset all or part of user data archive memory, follow these steps.
1. From the RAM ARCHIVE ALL menu, press ~ to display the ARCHIVE
menu.
2. Select one of the following:
1:Vars to display the RESET ARC VAR menu
TI-83 Plus
Memory and Variable Management
606
2:Apps to display the RESET ARC APPS menu.
3:Both to display the RESET ARC BOTH menu.
3. Read the message below the menu.
• To cancel the reset and return to the home screen, press Í.
• To continue with the reset, select 2:Reset. A message indicating
the type of archive memory cleared will be displayed on the home
screen.
TI-83 Plus
Memory and Variable Management
607
Resetting All Memory
When resetting all memory on the TI-83 Plus, RAM and user data
archive memory is restored to factory settings. All nonsystem variables,
applications, and programs are deleted. All system variables are reset to
default settings.
Tip: Before you reset all memory, consider restoring sufficient available
memory by deleting only selected data.
To reset all memory on the TI-83 Plus, follow these steps.
1. From the RAM ARCHIVE ALL menu, press ~ ~ to display the ALL menu.
2. Select 1:All Memory to display the RESET MEMORY menu.
TI-83 Plus
Memory and Variable Management
608
3. Read the message below the RESET MEMORY menu.
• To cancel the reset and return to the home screen, press Í.
• To continue with the reset, select 2:Reset. The message MEM
cleared is displayed on the home screen.
Note: When you clear memory, the contrast sometimes changes. If the screen
is faded or blank, adjust the contrast by pressing y } or †.
TI-83 Plus
Memory and Variable Management
609
Archiving and UnArchiving Variables
Archiving and UnArchiving Variables
Archiving allows you to store data, programs, or other variables to the
user data archive where they cannot be edited or deleted inadvertently.
Archiving also allows you to free up RAM for variables that may require
additional memory.
Archived variables cannot be edited or executed. They can only be seen
and unarchived. For example, if you archive list L1, you will see that L1
exists in memory but if you select it and paste the name L1 to the home
screen, you won’t be able to see its contents or edit it.
Note: Not all variables may be archived. Not all archived variables may be
unarchived. For example, system variables including r, t, x, y, and q cannot be
archived. Apps and Groups always exist in Flash ROM so there is no need to
archive them. Groups cannot be unarchived. However, you can ungroup or
delete them.
TI-83 Plus
Memory and Variable Management
610
Archive?
(yes/no)
UnArchive?
(yes/no)
Variable Type
Real numbers
Complex numbers
Matrices
Names
yes
yes
yes
yes
yes
yes
yes
yes
A, B, ... , Z
A, B, ... , Z
ãAä, ãBä, ãCä, ... , ãJä
Lists
L1, L2, L3, L4, L5, L6,
and user-defined
names
Programs
Functions
yes
no
yes
not
Y1, Y2, . . . , Y9, Y0
applicable
Parametric equations
no
not
X1T and Y1T, ... , X6T
applicable
and Y6T
Polar functions
Sequence functions
Stat plots
no
no
no
not
applicable
r1, r2, r3, r4, r5, r6
not
applicable
u, v, w
not
applicable
Plot1, Plot2, Plot3
GDB1, GDB2,...
Graph databases
Graph pictures
yes
yes
yes
yes
Pic1, Pic2, ... , Pic9,
Pic0
Strings
yes
yes
Str1, Str2, . . . Str9, Str0
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611
Archive?
(yes/no)
UnArchive?
(yes/no)
Variable Type
Names
Tables
no
not
TblStart, Tb1,
applicable
TblInput
Apps
see Note
above
no
Applications
AppVars
Groups
yes
yes
no
Application variables
see Note
above
Variables with reserved
names
no
not
applicable
minX, maxX, RegEQ,
and others
System variables
no
not
Xmin, Xmax, and
applicable
others
Archiving and unarchiving can be done in two ways:
• Use the 5:Archive or 6:UnArchive commands from the MEMORY menu
or CATALOG.
• Use a Memory Management editor screen.
Before archiving or unarchiving variables, particularly those with a large
byte size (such as large programs) use the MEMORY menu to:
• Find the size of the variable.
• See if there is enough free space.
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For:
Sizes must be such that:
Archive
UnArchive
Archive free size > variable size
RAM free size > variable size
Note: If there is not enough space, unarchive or delete variables as necessary.
Be aware that when you unarchive a variable, not all the memory associated
with that variable in user data archive will be released since the system keeps
track of where the variable has been and where it is now in RAM.
Even if there appears to be enough free space, you may see a Garbage
Collection message when you attempt to archive a variable. Depending
on the usability of empty blocks in the user data archive, you may need
to unarchive existing variables to create more free space.
To archive or unarchive a list variable (L1) using the Archive/UnArchive
options from the MEMORY menu:
1. Press y L to display the MEMORY menu.
2. Select 5:Archive or 6:UnArchive to place the command in the edit
screen.
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3. Press y d to place the L1 variable in the edit screen.
4. Press Í to complete the archive process.
Note: An asterisk will be displayed to the left of the Archived variable name to
indicate it is archived.
To archive or unarchive a list variable (L1) using a Memory Management
editor:
1. Press y L to display the MEMORY menu.
2. Select 2:Mem Mgmt/Del... to display the MEMORY MANAGEMENT/DELETE
menu.
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3. Select 4:List... to display the LIST menu.
4. Press Í to archive L1. An asterisk will appear to the left of L1 to
indicate it is an archived variable. To unarchive a variable in this
screen, put the cursor next to the archived variable and press Í.
The asterisk will disappear.
5. Press y 5 to leave the LIST menu.
Note: You can access an archived variable for the purpose of linking, deleting,
or unarchiving it, but you cannot edit it.
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Grouping and Ungrouping Variables
Grouping Variables
Grouping allows you to make a copy of two or more variables residing in
RAM and then store them as a group in user data archive. The variables
in RAM are not erased. The variables must exist in RAM before they can
be grouped. In other words, archived data cannot be included in a group.
To create a group of variables:
1. Press y L to display the MEMORY menu.
2. Select 8:Group... to display GROUP UNGROUP menu.
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3. Press Í to display the GROUP menu.
4. Enter a name for the new group and press Í.
Note: A group name can be one to eight characters long. The first character
must be a letter from A to Z or q. The second through eighth characters can
be letters, numbers, or q.
5. Select the type of data you want to group. You can select 1:All+ which
shows all variables of all types available and selected. You can also
select 1:All- which shows all variables of all types available but not
selected. A screen is displayed listing each variable of the type you
selected.
For example, suppose some variables have been created in RAM,
and selecting 1:All- displays the following screen.
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6. Press } and † to move the selection cursor (4) next to the first item
you want to copy into a group, and then press Í. A small square
will remain to the left of all variables selected for grouping.
Repeat the selection process until all variables for the new group are
selected and then press ~ to display the DONE menu.
7. Press Í to complete the grouping process.
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Note: You can only group variables in RAM. You cannot group some system
variables, such as the last-answer variable Ans and the statistical variable
RegEQ.
Ungrouping Variables
user data archive and place them ungrouped in RAM.
DuplicateName Menu
During the ungrouping action, if a duplicate variable name is detected in
RAM, the DUPLICATE NAME menu is displayed.
DuplicateName
1:Rename
Prompts to rename receiving variable.
2:Overwrite
3:Overwrite All
4:Omit
Overwrites data in receiving duplicate variable.
Overwrites data in all receiving duplicate variables.
Skips transmission of sending variable.
5:Quit
Stops transmission at duplicate variable.
Notes about Menu Items:
• When you select 1:Rename, the Name= prompt is displayed, and
alpha-lock is on. Enter a new variable name, and then press Í.
Ungrouping resumes.
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• When you select 2:Overwrite, the unit overwrites the data of the
duplicate variable name found in RAM. Ungrouping resumes.
• When you select 3: Overwrite All, the unit overwrites the data of all
duplicate variable names found in RAM. Ungrouping resumes.
• When you select 4:Omit, the unit does not ungroup the variable in
conflict with the duplicated variable name found in RAM. Ungrouping
resumes with the next item.
• When you select 5:Quit, ungrouping stops, and no further changes
are made.
To ungroup a group of variables:
1. Press y L to display the MEMORY menu.
2. Select 8:Group... to display the GROUP UNGROUP menu.
3. Press ~ to display the UNGROUP menu.
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4. Press } and † to move the selection cursor (4) next to the group
variable you want to ungroup, and then press Í.
The ungroup action is completed.
Note: Ungrouping does not remove the group from user data archive. You must
delete the group in user data archive to remove it.
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Garbage Collection
Garbage Collection Message
If you use the user data archive extensively, you may see a Garbage
Collect? message. This occurs if you try to archive a variable when there
is not enough free contiguous archive memory. The TI-83 Plus will
attempt to rearrange the archived variables to make additional room.
Responding to the Garbage Collection Message
• To cancel, select 1:No.
• If you choose 1:No, the message
ERR:ARCHIVE FULL will be displayed.
• To continue archiving, select 2:Yes.
If you select 2:Yes, the process message Garbage Collecting... or
Defragmenting... will be displayed.
Note: The process message Defragmenting... is displayed whenever an
application marked for deletion is encountered.
Garbage collection may take up to 20 minutes, depending on how much of
archive memory has been used to store variables.
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After garbage collection, depending on how much additional space is
freed, the variable may or may not be archived. If not, you can unarchive
some variables and try again.
Why Not Perform Garbage Collection Automatically Without a
Message?
The message:
• Lets you know an archive will take longer than usual. It also alerts
you that the archive will fail if there is not enough memory.
• Can alert you when a program is caught in a loop that repetitively fills
the user data archive. Cancel the archive and determine the reason.
Why Is Garbage Collection Necessary?
The user data archive is divided into sectors. When you first begin
archiving, variables are stored consecutively in sector 1. This continues
to the end of the sector.
An archived variable is stored in a continuous block within a single
sector. Unlike an application stored in user data archive, an archived
variable cannot cross a sector boundary. If there is not enough space left
in the sector, the next variable is stored at the beginning of the next
sector. Typically, this leaves an empty block at the end of the previous
sector.
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Each variable that you archive is stored in the first empty block large
enough to hold it.
Sector 1
variable A
variable B
Empty
block
Sector 2
variable D
variable C
Depending on its size,
variable D is stored in
one of these locations.
Sector 3
This process continues to the end of the last sector. Depending on the
size of individual variables, the empty blocks may account for a
significant amount of space. Garbage collection occurs when the
variable you are archiving is larger than any empty block.
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How Unarchiving a Variable Affects the Process
When you unarchive a variable, it is copied to RAM but it is not actually
deleted from user data archive memory.
Sector 1
variable A
After you unarchive
Sector 2
variables B and C, they
continue to take up
space.
variable D
Sector 3
Unarchived variables are “marked for deletion,” meaning they will be
deleted during the next garbage collection.
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If the MEMORY Screen Shows Enough Free Space
Even if the MEMORY screen shows enough free space to archive a
variable or store an application, you may still get a Garbage Collect?
message or an ERR: ARCHIVE FULL message.
When you unarchive a variable, the Archive free amount increases
immediately, but the space is not actually available until after the next
garbage collection.
If the Archive free amount shows enough available space for your
variable, there probably will be enough space to archive it after garbage
collection (depending on the usability of any empty blocks).
The Garbage Collection Process
Sector 1
variable A
The garbage collection process:
variable D
• Deletes unarchived variables from
the user data archive.
Sector 2
• Rearranges the remaining
variables into consecutive blocks.
Note: Power loss during garbage collection may cause all memory (RAM and
Archive) to be deleted.
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Using the GarbageCollect Command
You can reduce the number of automatic garbage collections by
periodically optimizing memory. This is done by using the GarbageCollect
command.
To use the GarbageCollect command, follow these steps.
1. Press y ãCATALOGä to display the CATALOG.
2. Press † or } to scroll the CATALOG until the selection cursor points to
the GarbageCollect command.
3. Press Í to paste the command to the current screen.
4. Press Í to display the Garbage Collect? message.
5. Select 2:Yes to begin garbage collection.
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ERR:ARCHIVE FULL Message
Even if the MEMORY screen shows enough free
space to archive a variable or store an
application, you may still get an ERR: ARCHIVE
FULL message.
An ERR:ARCHIVE FULL message may be displayed:
• When there is insufficient space to archive a variable within a
continuous block and within a single sector.
• When there is insufficient space to store an application within a
continuous block of memory.
When the message is displayed, it will indicate the largest single space
of memory available for storing a variable and an application.
To resolve the problem, use the GarbageCollect command to optimize
memory. If memory is still insufficient, you must delete variables or
applications to increase space.
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Chapter 19:
Communication Link
Getting Started: Sending Variables
Getting Started is a fast-paced introduction. Read the chapter for details.
Create and store a variable and a matrix, and then transfer them to another
TI-83 Plus.
1. On the home screen of the sending unit, press
5 Ë 5 ¿ ƒ Q. Press Í to store 5.5
to Q.
2. Press y H y H 1 ¢ 2 y I y H 3 ¢ 4
y I y I ¿ y > 1. Press Í
to store the matrix to [A].
3. On the sending unit, press y L to display
the MEMORY menu.
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4. On the sending unit, press 2 to select 2:Mem
Mgmt/Del. The MEMORY MANAGEMENT menu is
displayed.
5. On the sending unit, press 5 to select 5:Matrix.
The MATRIX editor screen is displayed.
6. On the sending unit, press Í to archive [A].
An asterisk ( ) will appear, signifying that [A] is
*
now archived.
7. Connect the calculators with the link cable.
Push both ends in firmly.
8. On the receiving unit, press y 8 ~ to
display the RECEIVE menu. Press 1 to select
1:Receive. The message Waiting... is displayed
and the busy indicator is on.
9. On the sending unit, press y 8 to display
the SEND menu.
10.Press 2 to select 2:AllN. The AllN SELECT screen
is displayed.
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11.Press † until the selection cursor ( 4 ) is next to
[A] MATRX. Press Í.
12.Press † until the selection cursor is next to
Q REAL. Press Í. A square dot next to [A]
and Q indicates that each is selected to send.
13.On the sending unit, press ~ to display the
TRANSMIT menu.
14.On the sending unit, press 1 to select 1:Transmit
and begin transmission. The receiving unit
displays the message Receiving....When the
items are transmitted, both units display the
name and type of each transmitted variable.
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631
TI-83 Plus Silver Edition LINK
This chapter describes how to communicate with compatible TI units. A
unit-to-unit link cable is included with the TI-83 Plus Silver Edition for this
purpose.
The TI-83 Plus Silver Edition has a port to connect and communicate
with:
• Another TI-83 Plus Silver Edition
• A TI-83 Plus
• A TI-83
• A TI-82
• A TI-73
• A CBL 2/CBL, or a CBR
With the TI™ Connect or TI-GRAPH LINK™ software and a TI-GRAPH LINK
cable, you can link the TI-83 Plus Silver Edition to a personal computer.
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632
Connecting Two Calculators with a Unit-to-Unit Cable
The TI-83 Plus link port is located at the center of the bottom edge of the
calculator.
1. Firmly insert either end of the unit-to-unit cable into the port.
2. Insert the other end of the cable into the other calculator’s port.
Linking to the CBL/CBR System
The CBL 2/CBL and the CBR are optional accessories that also connect
to a TI-83 Plus with the unit-to-unit link cable. With a CBL 2/CBL or CBR
and a TI-83 Plus, you can collect and analyze real-world data. The
software that enables this communication is built into the TI-83 Plus.
(Chapter 14).
Linking to a Computer
TI-GRAPH LINK™ is an accessory that links a TI-83 Plus to enable
communication with a computer. A Macintoshë-compatible
TI-GRAPH LINK is available separately.
You can access TI-GRAPH LINK guidebooks through
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633
Selecting Items to Send
LINK SEND Menu
To display the LINK SEND menu, press y 8.
SEND RECEIVE
1:All+...
Displays all items as selected, including RAM and Flash
applications.
2:AllN...
Displays all items as deselected.
Displays all program names.
3:Prgm...
4:List...
Displays all list names.
5:Lists to TI82...
6:GDB...
Displays list names L1 through L6.
Displays all graph databases.
Displays all picture data types.
Displays all matrix data types.
Displays all real variables.
7:Pic...
8:Matrix...
9:Real...
0:Complex...
A:Y-Vars...
B:String...
C:Apps...
Displays all complex variables.
Displays all Y= variables.
Displays all string variables.
Displays all software applications.
Displays all software application variables.
Displays all grouped variables.
Sends the Calculator ID number immediately. (You do not
need to select SEND.)
D:AppVars...
E:Group...
F:SendId
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SEND RECEIVE
G:SendOS
Sends operating system updates to another
TI-83 Plus Silver Edition or TI-83 Plus.
H:Back Up...
Selects all RAM and mode settings (no Flash applications
or archived items) for backup to another
TI-83 Plus Silver Edition or to a TI-83 Plus.
When you select an item on the LINK SEND menu, the corresponding
SELECT screen is displayed.
Note: Each SELECT screen, except All+…, is initially displayed with nothing pre-
selected. All+… is displayed with everything pre-selected.
To select items to send:
1. Press y 8 on the sending unit to display the LINK SEND menu.
2. Select the menu item that describes the data type to send. The
corresponding SELECT screen is displayed.
3. Press } and † to move the selection cursor ( 4 ) to an item you want
to select or deselect.
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4. Press Í to select or deselect the item. Selected names are
marked with a 0.
Note: An asterisk (*) to the left of an item indicates the item is archived
(Chapter 18).
5. Repeat steps 3 and 4 to select or deselect additional items.
Sending the Selected Items
After you have selected items to send on the sending unit and set the
receiving unit to receive, follow these steps to transmit the items. To set
1. Press ~ on the sending unit to display the TRANSMIT menu.
2. Confirm that Waiting... is displayed on the receiving unit, which
indicates it is set to receive.
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636
3. Press Í to select 1:Transmit. The name and type of each item are
displayed line-by-line on the sending unit as the item is queued for
transmission, and then on the receiving unit as each item is
accepted.
Note: Items sent from the RAM of the sending unit are transmitted to the
RAM of the receiving unit. Items sent from user data archive of the sending
unit are transmitted to user data archive of the receiving unit.
After all selected items have been transmitted, the message Done is
displayed on both calculators. Press } and † to scroll through the
names.
Stopping a Transmission
To stop a link transmission, press É. The Error in Xmit menu is displayed
on both units. To leave the error menu, select 1:Quit.
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Sending to a TI-83 Plus Silver Edition or TI-83 Plus
You can transfer variables (all types), programs, and Flash applications
to another TI-83 Plus Silver Edition or TI-83 Plus. You can also backup
the RAM memory of one unit to another.
Note: Keep in mind that the TI.83 Plus has less Flash memory than the
TI-83 Plus Silver Edition.
• Variables stored in RAM on the sending TI-83 Plus Silver Edition will
be sent to the RAM of the receiving TI-83 Plus Silver Edition or
TI-83 Plus.
• Variables and applications stored in the user data archive of the
sending TI-83 Plus Silver Edition will be sent to the user data archive
of the receiving TI-83 Plus Silver Edition or TI-83 Plus.
After sending or receiving data, you can repeat the same transmission to
additional TI-83 Plus Silver Edition or TI-83 Plus units—from either the
sending unit or the receiving unit—without having to reselect data to
send. The current items remain selected. However, you cannot repeat
transmission if you selected All+ or All..
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To send data to an additional TI-83 Plus Silver Edition or a TI-83 Plus:
1. Use a unit-to-unit cable to link two units together.
2. On the sending unit press y 8 and select a data type and items
to SEND.
3. Press ~ on the sending unit to display the TRANSMIT menu.
4. On the other unit, press y 8 ~ to display the RECEIVE menu.
5. Press Í on the receiving unit.
6. Press Í on the sending unit. A copy of the selected item(s) is
sent to the receiving unit.
7. Disconnect the link cable only from the receiving unit and connect it
to another unit.
8. Press y 8 on the sending unit.
9. Select only the data type. For example, if the unit just sent a list,
select 4:LIST.
Note: The item(s) you want to send are pre-selected from the last
transmission. Do not select or deselect any items. If you select or deselect
TI-83 Plus
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639
an item, all selections or deselections from the last transmission are
cleared.
10.Press ~ on the sending unit to display the TRANSMIT menu.
11.On the new receiving unit, press y 8 ~ to display the RECEIVE
menu.
12.Press Í on the receiving unit.
13.Press Í on the sending unit. A copy of the selected item(s) is
sent to the receiving unit.
14.Repeat steps 7 through 13 until the items are sent to all additional
units.
Sending to a TI-83
You can send all variables from a TI-83 Plus to a TI-83 except Flash
applications, application variables, grouped variables, new variable
types, or programs with new features in them (such as Archive,
UnArchive, Asm(, AsmComp, and AsmPrgm).
If archived variables on the TI-83 Plus are variable types recognized and
used on the TI-83, you can send these variables to the TI-83. They will
be automatically sent to the RAM of the TI-83 during the transfer
process.
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Note: You cannot perform a RAM memory backup from a TI-83 Plus to a TI-83
or from a TI-83 to a TI-83 Plus.
To send data to a TI-83:
1. Use a unit-to-unit cable to link the two units together.
2. Set the TI-83 to receive.
3. Press y 8 on the sending TI-83 Plus to display the LINK SEND
menu.
4. Select the menu of the items you want to transmit.
5. Press ~ on the sending TI-83 Plus to display the LINK TRANSMIT menu.
6. Confirm that the receiving unit is set to receive.
7. Press Í on the sending TI-83 Plus to select 1:Transmit and begin
transmitting.
Sending Lists to a TI-82
The only data type you can transmit from a TI-83 Plus to a TI-82 is real
list data stored in L1 through L6 (with up to 99 elements for each list). If
dimension is greater than 99 for a TI-83 Plus list that is selected to be
sent, the receiving TI-82 will truncate the list at the ninety-ninth element
during transmission.
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Note: You cannot perform a memory backup from a TI-83 Plus to a TI-82 or
from a TI-82 to a TI-83 Plus.
To send lists to a TI-82:
1. Use a unit-to-unit cable to link the two units together.
2. Set the TI-82 to receive.
3. Press y 8 5 on the sending TI-83 Plus to select 5:Lists to TI82.
The SELECT screen is displayed.
4. Select each list to transmit.
5. Press ~ to display the LINK TRANSMIT menu.
6. Confirm that the receiving unit is set to receive.
7. Press Í to select 1:Transmit and begin transmitting.
Sending to a TI-73
You can send real numbers, pics, real lists L1 through L6, and named
lists from a TI-73 to a TI-83 Plus or from a TI-83 Plus to a TI-73.
Since the Theta symbol (q) is not recognized by the TI-73, you cannot
include this symbol in any list names sent to the TI-73.
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Note: You cannot perform a RAM memory backup from a TI-83 Plus to a TI-73
or from a to a TI-73 to a TI-83 Plus.
To transmit data to a TI-73:
1. Use a unit-to-unit cable to link two units together.
2. Set the TI-73 to receive.
3. Press y 8 2 on the sending TI-83 Plus to select 2:All-.... The
SELECT screen is displayed.
4. Select items you want to send.
5. Press ~ on the sending TI-83 Plus to display the LINK TRANSMIT menu.
6. Confirm that the receiving unit is set to receive.
7. Press Í on the sending TI-83 Plus to select 1:Transmit and begin
transmitting.
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Receiving Items
LINK RECEIVE Menu
To display the LINK RECEIVE menu, press y 8 ~.
SENDRECEIVE
1:Receive
Sets unit to receive data transmission.
Receiving Unit
When you select 1:Receive from the LINK RECEIVE menu on the receiving
unit, the message Waiting... and the busy indicator are displayed. The
receiving unit is ready to receive transmitted items. To exit the receive
mode without receiving items, press É, and then select 1:Quit from the
Error in Xmit menu.
When transmission is complete, the unit exits the receive mode. You can
select 1:Receive again to receive more items. The receiving unit then
displays a list of items received. Press y 5 to exit the receive mode.
DuplicateName Menu
During transmission, if a variable name is duplicated, the DuplicateName
menu is displayed on the receiving unit.
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DuplicateName
1:Rename
2:Overwrite
3:Omit
Prompts to rename receiving variable.
Overwrites data in receiving variable.
Skips transmission of sending variable.
Stops transmission at duplicate variable.
4:Quit
When you select 1:Rename, the Name= prompt is displayed, and alpha-
lock is on. Enter a new variable name, and then press Í.
Transmission resumes.
When you select 2:Overwrite, the sending unit’s data overwrites the
existing data stored on the receiving unit. Transmission resumes.
When you select 3:Omit, the sending unit does not send the data in the
duplicated variable name. Transmission resumes with the next item.
When you select 4:Quit, transmission stops, and the receiving unit exits
receive mode.
Receiving from a TI-83 Plus Silver Edition or TI-83 Plus
The TI-83 Plus Silver Edition and the TI-83 Plus are totally compatible.
Keep in mind, however, that the TI-83 Plus has less Flash memory than
a TI-83 Plus Silver Edition.
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Receiving from a TI-83
You can transfer all variables and programs from a TI-83 to a TI-83 Plus
if they fit in the RAM of the TI-83 Plus. The RAM of the TI-83 Plus is
slightly less than the RAM of the TI-83.
Receiving from a TI-82 — Resolved Differences
Generally, you can transmit items to a TI-83 Plus from a TI-82, but
differences between the two products may affect some transmitted data.
This table shows differences for which the software built into the
TI-83 Plus automatically adjusts when a TI-83 Plus receives TI-82 data.
TI
.
82
TI-83 Plus
PlotStart
nMin
nMin
nStart
Un
u
Vn
v
UnStart
VnStart
TblMin
u(nMin)
v(nMin)
TblStart
For example, if you transmit a program that contains nStart on a
command line from a TI-82 to a TI-83 Plus, you will see that nMin has
automatically replaced nStart on the command line of the TI-83 Plus.
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Note: You can transfer all real variables, pics, and programs from a TI-82 to a
TI-83 Plus if they fit in the RAM of the TI-83 Plus. The RAM of the TI-83 Plus is
slightly less than the RAM of the TI-82.
Receiving from a TI-82 — Unresolved Differences
The software built into the TI-83 Plus cannot resolve some differences
between the TI-82 and TI-83 Plus. These differences are described
below.
You must edit the transmitted data on the receiving TI-83 Plus to account
for these differences. If you do not edit these differences, the TI-83 Plus
will misinterpret the data.
• The TI-83 Plus reinterprets TI-82 prefix functions to include open
parentheses, which may add extraneous parentheses to transmitted
expressions.
For example, if you transmit sin X+5 from a TI-82 to a TI-83 Plus, the
TI-83 Plus reinterprets it as sin(X+5. Without a closing parenthesis
after X, the TI-83 Plus interprets this as sin(X+5), not the sum of 5 and
sin(X).
• If a TI-82 transmits an instruction that the TI-83 Plus cannot translate,
the ERR:INVALID menu displays when the TI-83 Plus attempts to
execute the instruction.
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For example, on the TI-82, the character group Un-1 is pasted to the
cursor location when you press y [UnN1]. The TI-83 Plus cannot
directly translate Un-1 to the TI-83 Plus syntax u(nN1), so the
ERR:INVALID menu is displayed.
Note: TI-83 Plus implied multiplication rules differ from those of the TI-82.
For example, the TI-83 Plus evaluates 1à2X as (1à2)äX, while the TI-82
evaluates 1à2X as 1à(2äX) (Chapter 2).
Receiving from a TI-73
The TI-83 Plus can receive real numbers, pics, real lists L1 through L6,
and named lists from a TI-73.
Categorical lists (lists containing alpha characters as list elements)
cannot be sent from a TI-73 to a TI-83 Plus.
To transmit data to a TI-83 Plus from a TI-73:
1. Set the TI-83 Plus to receive.
2. Press Πon the sending TI-73 to display the APPLICATIONS menu.
3. Press Í on the sending TI-73 to select 1:Link and display the LINK
SEND menu.
4. Choose 0:Vars to TI83. and then select the items you want to send.
TI-83 Plus
Communication Link
648
5. Press ~ on the sending TI-73 to display the LINK TRANSMIT menu.
6. Confirm that the receiving unit is set to receive.
7. Press Í on the sending TI-73 to select 1:Transmit and begin
transmitting.
TI-83 Plus
Communication Link
649
Backing Up RAM Memory
Warning: H:Back Up overwrites the RAM memory and mode settings in
the receiving unit. All information in the RAM memory of the receiving
unit is lost.
Note: Archived items on the receiving unit are not overwritten.
You can backup the contents of RAM memory and mode settings (no
Flash applications or archived items) to another TI-83 Plus Silver Edition.
You can also backup RAM memory and mode settings to a TI-83 Plus.
To perform a RAM memory backup:
1. Use a unit-to-unit cable to link two TI-83 Plus Silver Edition units, or a
TI-83 Plus Silver Edition and a TI-83 Plus together.
2. On the sending unit press y 8 and select H:Back Up. The
MEMORYBACKUP screen displays.
3. On the receiving unit, press y 8 ~ to display the RECEIVE
menu.
4. Press Í on the receiving unit.
TI-83 Plus
Communication Link
650
5. Press Í on the sending unit. A WARNING — Backup message
displays on the receiving unit.
6. Press Í on the receiving unit to continue the backup.
— or —
Press 2:Quit on the receiving unit to cancel the backup and return to
the LINK SEND menu
Note: If a transmission error is returned during a backup, the receiving unit
is reset.
Memory Backup Complete
When the backup is complete, both the sending calculator and receiving
calculator display a confirmation screen.
TI-83 Plus
Communication Link
651
Error Conditions
A transmission error occurs after one or two seconds if:
• A cable is not attached to the sending unit.
• A cable is not attached to the receiving unit.
Note: If the cable is attached, push it in firmly and try again.
• The receiving unit is not set to receive transmission.
• You attempt a backup between a TI-73, a TI-82, or a TI-83 and a
TI-83 Plus.
• You attempt a data transfer from a TI-83 Plus to a TI-83, TI-82, or
TI-73 with variables or features not recognized by the TI-83, TI-82, or
TI-73.
• New variable types and features not recognized by the TI-83, TI-82,
or TI-73 include applications, application variables, grouped
variables, new variable types, or programs with new features in them
such as Archive, UnArchive, SendID, SendOS, Asm(, AsmComp(, and
AsmPrgm.
• You attempt a data transfer from a TI-83 Plus to a TI-82 with data
other than real lists L1 through L6 or without using menu item
5:Lists to TI82.
TI-83 Plus
Communication Link
652
• You attempt a data transfer from a TI-83 Plus to a TI-73 with data
other than real numbers, pics, real lists L1 through L6 or named lists
with q as part of the name.
Although a transmission error does not occur, these two conditions may
prevent successful transmission.
• You try to use Get( with a calculator instead of a CBL 2/CBL or CBR.
• You try to use GetCalc( with a TI-83 instead of a
TI-83 Plus Silver Edition or TI-83 Plus.
Insufficient Memory in Receiving Unit
During transmission, if the receiving unit does not have sufficient
memory to receive an item, the Memory Full menu is displayed on the
receiving unit.
• To skip this item for the current transmission, select 1:Omit.
Transmission resumes with the next item.
• To cancel the transmission and exit receive mode, select 2:Quit.
TI-83 Plus
Communication Link
653
Appendix A:
Tables and Reference Information
Table of Functions and Instructions
Functions return a value, list, or matrix. You can use functions in an
expression. Instructions initiate an action. Some functions and instructions
have arguments. Optional arguments and accompanying commas are
enclosed in brackets ( [ ] ). For details about an item, including argument
descriptions and restrictions, turn to the page listed on the right side of the
table.
From the CATALOG, you can paste any function or instruction to the home
screen or to a command line in the program editor. However, some
functions and instructions are not valid on the home screen. The items in
this table appear in the same order as they appear in the CATALOG.
† indicates either keystrokes that are valid in the program editor only or
ones that paste certain instructions when you are in the program editor.
Some keystrokes display menus that are available only in the program
editor. Others paste mode, format, or table-set instructions only when you
are in the program editor.
TI-83 Plus
Tables and Reference Information
654
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
abs(value)
Returns the absolute value of a real
number, expression, list, or matrix.
NUM
1:abs(
abs(complex value)
valueA and valueB
angle(value)
Returns the magnitude of a complex
number or list.
CPX
5:abs(
Returns 1 if both valueA and valueB
are ƒ 0. valueA and valueB can be
real numbers, expressions, or lists.
y :
LOGIC
1:and
Returns the polar angle of a complex
number or list of complex numbers.
CPX
4:angle(
ANOVA(list1,list2
[,list3,...,list20])
Performs a one-way analysis of
variance for comparing the means of
two to 20 populations.
…
TESTS
F:ANOVA(
Ans
Returns the last answer.
y Z
Archive
Moves the specified variables from
RAM to the user data archive
memory.
y L
5:Archive
Asm(assemblyprgmname) Executes an assembly language
y N
Asm(
program.
AsmComp(prgmASM1,
prgmASM2)
Compiles an assembly language
program written in ASCII and stores
the hex version.
y N
AsmComp(
AsmPrgm
Must be used as the first line of an
assembly language program.
y N
AsmPrgm
TI-83 Plus
Tables and Reference Information
655
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
augment(matrixA,
matrixB)
Returns a matrix, which is matrixB
appended to matrixA as new
columns.
y >
MATH
7:augment(
augment(listA,listB)
Returns a list, which is listB
concatenated to the end of listA.
y 9
OPS
9:augment(
AxesOff
Turns off the graph axes.
Turns on the graph axes.
† y .
AxesOff
AxesOn
† y .
AxesOn
a+bi
Sets the mode to rectangular
complex number mode (a+bi).
† z
a+bi
bal(npmt[,roundvalue])
Computes the balance at npmt for an Π1:Finance
amortization schedule using stored
values for PV, æ, and PMT and
rounds the computation to
roundvalue.
CALC
9:bal(
binomcdf(numtria)
Computes a cumulative probability at y =
x for the discrete binomial distribution DISTR
with the specified numtrials and
probability p of success on each trial.
A:binomcdf(
binompdf(numtrials,p[,x]) Computes a probability at x for the
y =
discrete binomial distribution with the DISTR
specified numtrials and probability p
of success on each trial.
0:binompdf(
TI-83 Plus
Tables and Reference Information
656
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2
2
c cdf(lowerbound,
Computes the c distribution
y =
DISTR
2
upperbound,df)
probability between lowerbound and
upperbound for the specified degrees 7:c cdf(
of freedom df.
2
c pdf(x,df)
Computes the probability density
function (pdf) for the c distribution at DISTR
a specified x value for the specified
degrees of freedom df.
Performs a chi-square test.
drawflag=1 draws results;
drawflag=0 calculates results.
y =
2
2
6:c pdf(
2
c .Test(observedmatrix,
† …
expectedmatrix
TESTS
2-
[,drawflag])
C:c Test(
Circle(X,Y,radius)
Clear Entries
ClrAllLists
ClrDraw
Draws a circle with center (X,Y) and
y <
DRAW
9:Circle(
radius.
Clears the contents of the Last Entry
storage area.
y L
MEMORY
3:Clear Entries
Sets to 0 the dimension of all lists in
memory.
y L
MEMORY
4:ClrAllLists
Clears all drawn elements from a
graph or drawing.
y <
DRAW
1:ClrDraw
ClrHome
Clears the home screen.
†
I/O
8:ClrHome
TI-83 Plus
Tables and Reference Information
657
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
ClrList listname1
[,listname2, ...,
listname n]
Sets to 0 the dimension of one or
more listnames.
…
EDIT
4:ClrList
ClrTable
Clears all values from the table.
†
I/O
9:ClrTable
conj(value)
Returns the complex conjugate of a
complex number or list of complex
numbers.
CPX
1:conj(
Connected
CoordOff
CoordOn
cos(value)
Sets connected plotting mode; resets † z
all Y= editor graph-style settings to ç .
Connected
Turns off cursor coordinate value
display.
† y .
CoordOff
Turns on cursor coordinate value
display.
† y .
CoordOn
Returns cosine of a real number,
expression, or list.
™
L1
cos (value)
Returns arccosine of a real number,
expression, or list.
y @
cosh(value)
Returns hyperbolic cosine of a real
number, expression, or list.
y N
cosh(
L1
cosh (value)
Returns hyperbolic arccosine of a
real number, expression, or list.
y N
cosh (
L1
CubicReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a cubic regression model to
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
6:CubicReg
TI-83 Plus
Tables and Reference Information
658
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
cumSum(list)
Returns a list of the cumulative sums y 9
of the elements in list, starting with
OPS
6:cumSum(
the first element.
cumSum(matrix)
Returns a matrix of the cumulative
sums of matrix elements. Each
element in the returned matrix is a
cumulative sum of a matrix column
from top to bottom.
y >
MATH
0:cumSum(
dbd(date1,date2)
Calculates the number of days
between date1 and date2 using the
actual-day-count method.
Π1:Finance
CALC
D:dbd(
value4Dec
Displays a real or complex number,
expression, list, or matrix in decimal
format.
MATH
2:4Dec
Degree
Sets degree angle mode.
† z
Degree
DelVar variable
Deletes from memory the contents of †
variable.
CTL
G:DelVar
DependAsk
DependAuto
det(matrix)
Sets table to ask for dependent-
variable values.
† y -
Depend: Ask
Sets table to generate dependent-
variable values automatically.
† y -
Depend: Auto
Returns determinant of matrix.
y >
MATH
1:det(
TI-83 Plus
Tables and Reference Information
659
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2
DiagnosticOff
Sets diagnostics-off mode; r, r , and
y N
DiagnosticOff
2
R are not displayed as regression
model results.
2
DiagnosticOn
Sets diagnostics-on mode; r, r , and
y N
DiagnosticOn
2
R are displayed as regression
model results.
dim(listname)
Returns the dimension of listname.
y 9
OPS
3:dim(
dim(matrixname)
length!dim(listname)
Returns the dimension of
matrixname as a list.
y >
MATH
3:dim(
Assigns a new dimension (length) to a y 9
new or existing listname.
OPS
3:dim(
{rows,columns}!
dim(matrixname)
Assigns new dimensions to a new or
existing matrixname.
y >
MATH
3:dim(
Disp
Displays the home screen.
Displays each value.
Displays the graph.
†
I/O
3:Disp
Disp [valueA,valueB,
valueC,...,value n]
†
I/O
3:Disp
DispGraph
†
I/O
4:DispGraph
TI-83 Plus
Tables and Reference Information
660
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
DispTable
Displays the table.
†
I/O
5:DispTable
value4DMS
Displays value in DMS format.
y ;
ANGLE
4:4DMS
Dot
Sets dot plotting mode; resets all Y=
editor graph-style settings to í .
† z
Dot
DrawF expression
Draws expression (in terms of X) on
the graph.
y <
DRAW
6:DrawF
DrawInv expression
Draws the inverse of expression by
plotting X values on the y-axis and Y
values on the x-axis.
y <
DRAW
8:DrawInv
:DS<(variable,value)
:commandA
:commands
Decrements variable by 1; skips
commandA if variable < value.
†
CTL
B:DS<(
e^(power)
e^(list)
Returns e raised to power.
Returns a list of e raised to a list of
powers.
y J
y J
Exponent:
valueEexponent
Exponent:
listEexponent
Exponent:
matrixEexponent
Returns value times 10 to the
y D
y D
y D
exponent.
Returns list elements times 10 to the
exponent.
Returns matrix elements times 10 to
the exponent.
TI-83 Plus
Tables and Reference Information
661
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
4Eff(nominal rate,
compounding periods)
Computes the effective interest rate.
Π1:Finance
CALC
C:4Eff(
Else
See If:Then:Else
End
Identifies end of For(, If-Then-Else,
Repeat, or While loop.
†
CTL
7:End
Eng
Sets engineering display mode.
† z
Eng
Equ4String(Y= var,Strn)
expr(string)
Converts the contents of a Y= var to
y N
Equ4String(
a string and stores it in Strn.
Converts string to an expression and y N
executes it.
expr(
ExpReg [Xlistname,
Ylistname,freqlist,regequ]
Fits an exponential regression model
to Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
0:ExpReg
ExprOff
ExprOn
Turns off the expression display
during TRACE.
† y .
ExprOff
Turns on the expression display
during TRACE.
† y .
ExprOn
Ücdf(lowerbound,
upperbound,
Computes the Û distribution
probability between lowerbound and
upperbound for the specified
numerator df (degrees of freedom)
and denominator df.
y =
DISTR
9:Ûcdf(
numerator df,
denominator df)
TI-83 Plus
Tables and Reference Information
662
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Fill(value,matrixname)
Fill(value,listname)
Fix #
Stores value to each element in
y >
matrixname.
MATH
4:Fill(
Stores value to each element in
listname.
y 9
OPS
4:Fill(
Sets fixed-decimal mode for # of
decimal places.
† z
0123456789
(select one)
Float
Sets floating decimal mode.
† z
Float
fMax(expression,variable, Returns the value of variable where
lower,upper[,tolerance]) the local maximum of expression
occurs, between lower and upper,
MATH
7:fMax(
with specified tolerance.
fMin(expression,variable,
Returns the value of variable where
MATH
6:fMin(
lower,upper[,tolerance]) the local minimum of expression
occurs, between lower and upper,
with specified tolerance.
fnInt(expression,variable, Returns the function integral of
lower,upper[,tolerance]) expression with respect to variable,
between lower and upper, with
MATH
9:fnInt(
specified tolerance.
FnOff [function#,
function#,...,function n]
Deselects all Y= functions or
specified Y= functions.
Y-VARS On/Off
2:FnOff
TI-83 Plus
Tables and Reference Information
663
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
FnOn [function#,
function#,...,function n]
Selects all Y= functions or specified
Y= functions.
Y-VARS On/Off
1:FnOn
:For(variable,begin,end
[,increment])
:commands
Executes commands through End,
incrementing variable from begin by
increment until variable>end.
†
CTL
4:For(
:End
:commands
fPart(value)
Returns the fractional part or parts of
a real or complex number,
NUM
expression, list, or matrix.
4:fPart(
Üpdf(x,numerator df,
denominator df)
Computes the Û distribution
probability between lowerbound and
upperbound for the specified
numerator df (degrees of freedom)
and denominator df.
y =
DISTR
8:Ûpdf(
value4Frac
Displays a real or complex number,
expression, list, or matrix as a fraction MATH
simplified to its simplest terms.
1:4Frac
Full
Sets full screen mode.
† z
Full
Func
Sets function graphing mode.
† z
Func
GarbageCollect
Displays the garbage collection
menu to allow cleanup of unused
archive memory.
y N
GarbageCollect
TI-83 Plus
Tables and Reference Information
664
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
gcd(valueA,valueB)
Returns the greatest common divisor
of valueA and valueB, which can be
real numbers or lists.
NUM
9:gcd(
geometcdf(p,x)
Computes a cumulative probability at y =
x, the number of the trial on which
DISTR
E:geometcdf(
the first success occurs, for the
discrete geometric distribution with
the specified probability of success p.
geometpdf(p,x)
Computes a probability at x, the
number of the trial on which the first
success occurs, for the discrete
geometric distribution with the
specified probability of success p.
y =
DISTR
D:geometpdf(
Get(variable)
GetCalc(variable)
getKey
Gets data from the CBL 2™/CBL™ or †
CBR™ System and stores it in variable. I/O
A:Get(
Gets contents of variable on another
TI-83 Plus and stores it to variable on
the receiving TI-83 Plus.
†
I/O
0:GetCalc(
Returns the key code for the current
keystroke, or 0, if no key is pressed.
†
I/O
7:getKey
Goto label
Transfers control to label.
†
CTL
0:Goto
GraphStyle(function#,
graphstyle#)
Sets a graphstyle for function#.
†
CTL
H:GraphStyle(
TI-83 Plus
Tables and Reference Information
665
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
GridOff
GridOn
G-T
Turns off grid format.
† y .
GridOff
Turns on grid format.
† y .
GridOn
Sets graph-table vertical split-screen
mode.
† z
G-T
Horiz
Sets horizontal split-screen mode.
† z
Horiz
Horizontal y
Draws a horizontal line at y.
y <
DRAW
3:Horizontal
identity(dimension)
Returns the identity matrix of
dimension rows × dimension
columns.
y >
MATH
5:identity(
:If condition
:commandA
:commands
If condition = 0 (false), skips
commandA.
†
CTL
1:If
:If condition
:Then
:commands
:End
Executes commands from Then to
End if condition = 1 (true).
†
CTL
2:Then
:commands
TI-83 Plus
Tables and Reference Information
666
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
:If condition
:Then
:commands
:Else
Executes commands from Then to
Else if condition = 1 (true); from Else
to End if condition = 0 (false).
†
CTL
3:Else
:commands
:End
:commands
imag(value)
Returns the imaginary (nonreal) part
of a complex number or list of
complex numbers.
CPX
3:imag(
IndpntAsk
IndpntAuto
Input
Sets table to ask for independent-
variable values.
† y -
Indpnt: Ask
Sets table to generate independent-
variable values automatically.
† y -
Indpnt: Auto
Displays graph.
†
I/O
1:Input
Input [variable]
Input ["text",variable]
Prompts for value to store to
variable.
†
I/O
1:Input
Input [Strn,variable]
Displays Strn and stores entered
value to variable.
†
I/O
1:Input
inString(string,substring
[,start])
Returns the character position in
string of the first character of
substring beginning at start.
y N
inString(
TI-83 Plus
Tables and Reference Information
667
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
int(value)
Returns the largest integer a real or
complex number, expression, list, or
matrix.
NUM
5:int(
GInt(pmt1,pmt2
[,roundvalue])
Computes the sum, rounded to
roundvalue, of the interest amount
between pmt1 and pmt2 for an
amortization schedule.
Π1:Finance
CALC
A:GInt(
invNorm(area[,m,s])
Computes the inverse cumulative
normal distribution function for a
given area under the normal
distribution curve specified by m and
s.
y =
DISTR
3:invNorm(
iPart(value)
Returns the integer part of a real or
complex number, expression, list, or
matrix.
NUM
3:iPart(
irr(CF0,CFList[,CFFreq])
:IS>(variable,value)
:commandA
:commands
Returns the interest rate at which the Π1:Finance
net present value of the cash flow is
equal to zero.
CALC
8:irr(
Increments variable by 1; skips
commandA if variable>value.
†
CTL
A:IS>(
Ùlistname
Identifies the next one to five
characters as a user-created list
name.
y 9
OPS
B:(
LabelOff
LabelOn
Turns off axes labels.
† y .
LabelOff
Turns on axes labels.
† y .
LabelOn
TI-83 Plus
Tables and Reference Information
668
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Lbl label
Creates a label of one or two
characters.
†
CTL
9:Lbl
lcm(valueA,valueB)
Returns the least common multiple of
valueA and valueB, which can be
real numbers or lists.
NUM
8:lcm(
length(string)
Returns the number of characters in
string.
y N
length(
Line(X1,Y1,X2,Y2)
Draws a line from (X1,Y1) to (X2,Y2). y <
DRAW
2:Line(
Line(X1,Y1,X2,Y2,0)
Erases a line from (X1,Y1) to
(X2,Y2).
y <
DRAW
2:Line(
LinReg(a+bx) [Xlistname, Fits a linear regression model to
…
CALC
8:LinReg(a+bx)
Ylistname,freqlist,
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
regequ]
LinReg(ax+b) [Xlistname, Fits a linear regression model to
…
CALC
4:LinReg(ax+b)
Ylistname,freqlist,
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
regequ]
LinRegTTest [Xlistname,
Ylistname,freqlist,
alternative,regequ]
Performs a linear regression and a
t-test. alternative=L1 is <;
alternative=0 is ƒ; alternative=1 is >.
† …
TESTS
E:LinRegTTest
@List(list)
Returns a list containing the
differences between consecutive
elements in list.
y 9
OPS
7:@List(
TI-83 Plus
Tables and Reference Information
669
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
List4matr(listname1,...,
listname n,matrixname)
Fills matrixname column by column
y 9
with the elements from each specified OPS
listname.
0:List4matr(
ln(value)
Returns the natural logarithm of a
real or complex number, expression,
or list.
µ
LnReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a logarithmic regression model
to Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
9:LnReg
log(value)
Returns logarithm of a real or
complex number, expression, or list.
«
Logistic [Xlistname,
Ylistname,freqlist,
regequ]
Fits a logistic regression model to
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
B:Logistic
Matr4list(matrix,
Fills each listname with elements
y 9
OPSA:Matr4list(
listnameA,...,listname n) from each column in matrix.
Matr4list(matrix,
column#,listname)
Fills a listname with elements from a
specified column# in matrix.
y 9
OPSA:Matr4list(
max(valueA,valueB)
Returns the larger of valueA and
valueB.
NUM
7:max(
max(list)
Returns largest real or complex
element in list.
y 9
MATH
2:max(
TI-83 Plus
Tables and Reference Information
670
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
max(listA,listB)
Returns a real or complex list of the
larger of each pair of elements in listA MATH
and listB.
y 9
2:max(
max(value,list)
Returns a real or complex list of the
larger of value or each list element.
y 9
MATH
2:max(
mean(list[,freqlist])
median(list[,freqlist])
Returns the mean of list with
y 9
MATH
3:mean(
frequency freqlist.
Returns the median of list with
frequency freqlist.
y 9
MATH
4:median(
Med-Med [Xlistname,
Ylistname,freqlist,
regequ]
Fits a median-median model to
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
3:Med-Med
Menu("title","text1",label1 Generates a menu of up to seven
†
CTL
C:Menu(
[,...,"text7",label7])
items during program execution.
min(valueA,valueB)
Returns smaller of valueA and
valueB.
NUM
6:min(
min(list)
Returns smallest real or complex
element in list.
y 9
MATH
1:min(
min(listA,listB)
Returns real or complex list of the
smaller of each pair of elements in
listA and listB.
y 9
MATH
1:min(
TI-83 Plus
Tables and Reference Information
671
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
min(value,list)
valueA nCr valueB
value nCr list
Returns a real or complex list of the
smaller of value or each list element. MATH
y 9
1:min(
Returns the number of combinations
of valueA taken valueB at a time.
PRB
3:nCr
Returns a list of the combinations of
value taken each element in list at a
time.
PRB
3:nCr
list nCr value
Returns a list of the combinations of
each element in list taken value at a
time.
PRB
3:nCr
listA nCr listB
Returns a list of the combinations of
each element in listA taken each
element in listB at a time.
PRB
3:nCr
nDeriv(expression,variable, Returns approximate numerical
MATH
8:nDeriv(
value[,H])
derivative of expression with respect
to variable at value, with specified H.
4Nom(effective rate,
Computes the nominal interest rate.
Sets normal display mode.
Π1:Finance
CALC
B:4Nom(
compounding periods)
Normal
† z
Normal
normalcdf(lowerbound,
upperbound[,m,s])
Computes the normal distribution
probability between lowerbound and
upperbound for the specified m and
s.
y =
DISTR
2:normalcdf(
TI-83 Plus
Tables and Reference Information
672
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
normalpdf(x[,m,s])
Computes the probability density
function for the normal distribution at
y =
DISTR
a specified x value for the specified m 1:normalpdf(
and s.
not(value)
Returns 0 if value is ƒ 0. value can
be a real number, expression, or list.
y :
LOGIC
4:not(
valueA nPr valueB
value nPr list
list nPr value
listA nPr listB
Returns the number of permutations
of valueA taken valueB at a time.
PRB
2:nPr
Returns a list of the permutations of
value taken each element in list at a
time.
PRB
2:nPr
Returns a list of the permutations of
each element in list taken value at a
time.
PRB
2:nPr
Returns a list of the permutations of
each element in listA taken each
element in listB at a time.
PRB
2:nPr
npv(interest rate,CF0,
CFList[,CFFreq])
Computes the sum of the present
values for cash inflows and outflows.
Π1:Finance
CALC
7:npv(
valueA or valueB
Returns 1 if valueA or valueB is ƒ 0.
valueA and valueB can be real
numbers, expressions, or lists.
y :
LOGIC
2:or
Output(row,column,
"text")
Displays text beginning at specified
row and column.
†
I/O
6:Output(
TI-83 Plus
Tables and Reference Information
673
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Output(row,column,
value)
Displays value beginning at specified †
row and column.
I/O
6:Output(
Param
Pause
Sets parametric graphing mode.
† z
Par
Suspends program execution until
you press Í.
†
CTL
8:Pause
Pause [value]
Displays value; suspends program
execution until you press Í.
†
CTL
8:Pause
Plot#(type,Xlistname,
Ylistname,mark)
Defines Plot# (1, 2, or 3) of type
Scatter or xyLine for Xlistname and
Ylistname using mark.
† y ,
PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
Plot#(type,Xlistname,
freqlist)
Defines Plot# (1, 2, or 3) of type
Histogram or Boxplot for Xlistname
with frequency freqlist.
† y ,
PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
Plot#(type,Xlistname,
freqlist,mark)
Defines Plot# (1, 2, or 3) of type
ModBoxplot for Xlistname with
frequency freqlist using mark.
† y ,
PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
TI-83 Plus
Tables and Reference Information
674
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Plot#(type,datalistname,
data axis,mark)
Defines Plot# (1, 2, or 3) of type
NormProbPlot for datalistname on
data axis using mark. data axis can
be X or Y.
† y ,
PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
PlotsOff [1,2,3]
PlotsOn [1,2,3]
Pmt_Bgn
Deselects all stat plots or one or
more specified stat plots (1, 2, or 3).
y ,
STAT PLOTS
4:PlotsOff
Selects all stat plots or one or more
specified stat plots (1, 2, or 3).
y ,
STAT PLOTS
5:PlotsOn
Specifies an annuity due, where
payments occur at the beginning of
each payment period.
Π1:Finance
CALC
F:Pmt_Bgn
Pmt_End
Specifies an ordinary annuity, where
payments occur at the end of each
payment period.
Π1:Finance
CALC
E:Pmt_End
poissoncdf(m,x)
poissonpdf(m,x)
Computes a cumulative probability at y =
x for the discrete Poisson distribution DISTR
with specified mean m.
C:poissoncdf(
Computes a probability at x for the
discrete Poisson distribution with the
specified mean m.
y =
DISTR
B:poissonpdf(
Polar
Sets polar graphing mode.
† z
Pol
complex value 4Polar
Displays complex value in polar
format.
CPX
7:4Polar
TI-83 Plus
Tables and Reference Information
675
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
PolarGC
Sets polar graphing coordinates
format.
† y .
PolarGC
prgmname
Executes the program name.
†
CTRL
D:prgm
GPrn(pmt1,pmt2
[,roundvalue])
Computes the sum, rounded to
roundvalue, of the principal amount
between pmt1 and pmt2 for an
amortization schedule.
Π1:Finance
CALC
0:GPrn(
prod(list[,start,end])
Returns product of list elements
between start and end.
y 9
MATH
6:prod(
Prompt variableA
Prompts for value for variableA, then †
[,variableB,...,variable n] variableB, and so on.
I/O
2:Prompt
1.PropZInt(x,n
[,confidence level])
Computes a one-proportion z
confidence interval.
† …
TESTS
A:1-PropZInt(
2.PropZInt(x1,n1,x2,n2
[,confidence level])
Computes a two-proportion z
confidence interval.
† …
TESTS
B:2-PropZInt(
1.PropZTest(p0,x,n
[,alternative,drawflag])
Computes a one-proportion z test.
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. drawflag=1
draws results; drawflag=0 calculates
results.
† …
TESTS
5:1-PropZTest(
TI-83 Plus
Tables and Reference Information
676
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2.PropZTest(x1,n1,x2,n2
[,alternative,drawflag])
Computes a two-proportion z test.
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. drawflag=1
draws results; drawflag=0 calculates
results.
† …
TESTS
6:2-PropZTest(
Pt.Change(x,y)
Pt.Off(x,y[,mark])
Pt.On(x,y[,mark])
Reverses a point at (x,y).
y <
POINTS
3:Pt.Change(
Erases a point at (x,y) using mark.
Draws a point at (x,y) using mark.
y <
POINTS
2:Pt.Off(
y <
POINTS
1:Pt.On(
PwrReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a power regression model to
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
A:PwrReg
Pxl.Change(row,column) Reverses pixel at (row,column);
y <
POINTS
6:Pxl.Change(
0 row 62 and 0 column 94.
Pxl.Off(row,column)
Erases pixel at (row,column);
0 row 62 and 0 column 94.
y <
POINTS
5:Pxl.Off(
Pxl.On(row,column)
Draws pixel at (row,column);
0 row 62 and 0 column 94.
y <
POINTS
4:Pxl.On(
TI-83 Plus
Tables and Reference Information
677
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
pxl.Test(row,column)
Returns 1 if pixel (row, column) is on, y <
0 if it is off; 0 row 62 and
POINTS
0 column 94.
7:pxl.Test(
P4Rx(r,q)
Returns X, given polar coordinates r
and q or a list of polar coordinates.
y ;
ANGLE
7:P4Rx(
P4Ry(r,q)
Returns Y, given polar coordinates r
and q or a list of polar coordinates.
y ;
ANGLE
8:P4Ry(
QuadReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a quadratic regression model to
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
5:QuadReg
QuartReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a quartic regression model to
Xlistname and Ylistname with
frequency freqlist, and stores the
regression equation to regequ.
…
CALC
7:QuartReg
Radian
Sets radian angle mode.
† z
Radian
rand[(numtrials)]
Returns a random number between 0
and 1 for a specified number of trials PRB
numtrials.
1:rand
randBin(numtrials,prob
[,numsimulations])
Generates and displays a random
real number from a specified
Binomial distribution.
PRB
7:randBin(
TI-83 Plus
Tables and Reference Information
678
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
randInt( lower,upper
[,numtrials])
Generates and displays a random
integer within a range specified by
lower and upper integer bounds for a 5:randInt(
specified number of trials numtrials.
PRB
randM(rows,columns)
Returns a random matrix of rows (1– y >
99) × columns (1–99).
MATH
6:randM(
randNorm(m,s[,numtrials]) Generates and displays a random
PRB
real number from a specified Normal
distribution specified by m and s for a 6:randNorm(
specified number of trials numtrials.
re^qi
Sets the mode to polar complex
number mode (re^qi).
† z
re^qi
Real
Sets mode to display complex results † z
only when you enter complex
numbers.
Real
real(value)
Returns the real part of a complex
number or list of complex numbers.
CPX
2:real(
RecallGDB n
RecallPic n
Restores all settings stored in the
graph database variable GDBn.
y <
STO
4:RecallGDB
Displays the graph and adds the
picture stored in Picn.
y <
STO
2:RecallPic
complex value 4Rect
Displays complex value or list in
rectangular format.
CPX
6:4Rect
TI-83 Plus
Tables and Reference Information
679
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
RectGC
Sets rectangular graphing
coordinates format.
† y .
RectGC
ref(matrix)
Returns the row-echelon form of a
matrix.
y >
MATH
A:ref(
:Repeat condition
:commands
:End
Executes commands until condition
is true.
†
CTL
6:Repeat
:commands
Return
Returns to the calling program.
†
CTL
E:Return
round(value[,#decimals])
ärow(value,matrix,row)
row+(matrix,rowA,rowB)
Returns a number, expression, list,
or matrix rounded to #decimals ( 9). NUM
2:round(
y >
multiplied by value and stored in row. MATH
E:ärow(
Returns a matrix with row of matrix
Returns a matrix with rowA of matrix
added to rowB and stored in rowB.
y >
MATH
D:row+(
ärow+(value,matrix,
rowA,rowB)
Returns a matrix with rowA of matrix y >
multiplied by value, added to rowB,
MATH
and stored in rowB.
F:ärow+(
rowSwap(matrix,rowA,
rowB)
Returns a matrix with rowA of matrix y >
swapped with rowB.
MATH
C:rowSwap(
TI-83 Plus
Tables and Reference Information
680
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
rref(matrix)
Returns the reduced row-echelon
form of a matrix.
y >
MATH
B:rref(
R4Pr(x,y)
Returns R, given rectangular
coordinates x and y or a list of
rectangular coordinates.
y ;
ANGLE
5:R4Pr(
R4Pq(x,y)
Returns q, given rectangular
coordinates x and y or a list of
rectangular coordinates.
y ;
ANGLE
6:R4Pq(
2.SampÜTest [listname1, Performs a two-sample Û test.
† …
TESTS
D:2-SampÛTest
listname2,freqlist1,
freqlist2,alternative,
drawflag]
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. drawflag=1
draws results; drawflag=0 calculates
results.
(Data list input)
2.SampÜTest Sx1,n1,
Sx2,n2[,alternative,
drawflag]
Performs a two-sample Û test.
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. drawflag=1
draws results; drawflag=0 calculates
results.
† …
TESTS
D:2-SampÛTest
(Summary stats input)
2.SampTInt [listname1,
listname2,
freqlist1,freqlist2,
confidence level,pooled]
(Data list input)
Computes a two-sample t confidence † …
interval. pooled=1 pools variances;
TESTS
pooled=0 does not pool variances.
0:2-SampTInt
2.SampTInt v1,Sx1,n1,
Computes a two-sample t confidence † …
v2,Sx2,n2
interval. pooled=1 pools variances;
TESTS
[,confidence level,pooled] pooled=0 does not pool variances.
(Summary stats input)
0:2-SampTInt
TI-83 Plus
Tables and Reference Information
681
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2.SampTTest [listname1,
listname2,freqlist1,
freqlist2,alternative,
pooled,drawflag]
Computes a two-sample t test.
† …
TESTS
4:2-SampTTest
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. pooled=1 pools
variances; pooled=0 does not pool
variances. drawflag=1 draws results;
drawflag=0 calculates results.
(Data list input)
2.SampTTest v1,Sx1,n1,
v2,Sx2,n2[,alternative,
pooled,drawflag]
Computes a two-sample t test.
† …
TESTS
4:2-SampTTest
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. pooled=1 pools
variances; pooled=0 does not pool
variances. drawflag=1 draws results;
drawflag=0 calculates results.
(Summary stats input)
2.SampZInt(s1,s2
[,listname1,listname2,
freqlist1,freqlist2,
confidence level])
(Data list input)
Computes a two-sample z
confidence interval.
† …
TESTS
9:2-SampZInt(
2.SampZInt(s1,s2,
v1,n1,v2,n2
[,confidence level])
(Summary stats input)
Computes a two-sample z
confidence interval.
† …
TESTS
9:2-SampZInt(
2.SampZTest(s1,s2
[,listname1,listname2,
freqlist1,freqlist2,
alternative,drawflag])
(Data list input)
Computes a two-sample z test.
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. drawflag=1
† …
TESTS
draws results; drawflag=0 calculates 3:2-SampZTest(
results.
TI-83 Plus
Tables and Reference Information
682
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2.SampZTest(s1,s2,
v1,n1,v2,n2
[,alternative,drawflag])
(Summary stats input)
Computes a two-sample z test.
alternative=L1 is <; alternative=0 is
ƒ; alternative=1 is >. drawflag=1
† …
TESTS
draws results; drawflag=0 calculates 3:2-SampZTest(
results.
Sci
Sets scientific notation display mode. † z
Sci
Select(Xlistname,
Ylistname)
Selects one or more specific data
points from a scatter plot or xyLine
plot (only), and then stores the
selected data points to two new lists,
Xlistname and Ylistname.
y 9
OPS
8:Select(
Send(variable)
Sends contents of variable to the
CBL 2/CBL or CBR System.
†
I/O
B:Send(
seq(expression,variable,
begin,end[,increment])
Returns list created by evaluating
expression with regard to variable,
from begin to end by increment.
y 9
OPS
5:seq(
Seq
Sets sequence graphing mode.
† z
Seq
Sequential
SetUpEditor
Sets mode to graph functions
sequentially.
† z
Sequential
Removes all list names from the stat
list editor, and then restores list
names L1 through L6 to columns 1
through 6.
…
EDIT
5:SetUpEditor
TI-83 Plus
Tables and Reference Information
683
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
SetUpEditor listname1
[,listname2,...,
listname20]
Removes all list names from the stat
list editor, then sets it up to display
one or more listnames in the
specified order, starting with column
1.
…
EDIT
5:SetUpEditor
Shade(lowerfunc,
upperfunc[,Xleft,Xright,
pattern,patres])
Draws lowerfunc and upperfunc in
y <
DRAW
terms of X on the current graph and
uses pattern and patres to shade the 7:Shade(
area bounded by lowerfunc,
upperfunc, Xleft, and Xright.
2
2
Shadec (lowerbound,
Draws the density function for the c
distribution specified by degrees of
freedom df and shades the area
between lowerbound and
y =
DRAW
3:Shadec (
upperbound,df)
2
upperbound.
ShadeÜ(lowerbound,
upperbound,
Draws the density function for the Û
distribution specified by numerator df DRAW
and denominator df and shades the
area between lowerbound and
upperbound.
y =
numerator df,
4:ShadeÜ(
denominator df)
ShadeNorm(lowerbound, Draws the normal density function
y =
DRAW
1:ShadeNorm(
upperbound[,m,s])
specified by m and s and shades the
area between lowerbound and
upperbound.
Shade_t(lowerbound,
upperbound,df)
Draws the density function for the
Student-t distribution specified by
degrees of freedom df, and shades
the area between lowerbound and
upperbound.
y =
DRAW
2:Shade_t(
TI-83 Plus
Tables and Reference Information
684
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Simul
Sets mode to graph functions
simultaneously.
† z
Simul
sin(value)
Returns the sine of a real number,
expression, or list.
˜
L1
sin (value)
Returns the arcsine of a real number, y ?
expression, or list.
sinh(value)
Returns the hyperbolic sine of a real
number, expression, or list.
y N
sinh(
L1
sinh (value)
Returns the hyperbolic arcsine of a
real number, expression, or list.
y N
sinh (
L1
SinReg [iterations,
Xlistname,Ylistname,
period,regequ]
Attempts iterations times to fit a
sinusoidal regression model to
Xlistname and Ylistname using a
period guess, and stores the
regression equation to regequ.
…
CALC
C:SinReg
solve(expression,variable, Solves expression for variable, given †
guess,{lower,upper})
an initial guess and lower and upper
bounds within which the solution is
sought.
MATH
0:solve(
SortA(listname)
Sorts elements of listname in
ascending order.
y 9
OPS1:SortA(
SortA(keylistname,
Sorts elements of keylistname in
y 9
OPS
1:SortA(
dependlist1[,dependlist2, ascending order, then sorts each
...,dependlist n])
dependlist as a dependent list.
SortD(listname)
Sorts elements of listname in
descending order.
y 9
OPS2:SortD(
TI-83 Plus
Tables and Reference Information
685
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
SortD(keylistname,
Sorts elements of keylistname in
y 9
OPS
2:SortD(
dependlist1[,dependlist2, descending order, then sorts each
..., dependlist n])
dependlist as a dependent list.
stdDev(list[,freqlist])
Returns the standard deviation of the y 9
elements in list with frequency
MATH
7:stdDev(
freqlist.
Stop
Ends program execution; returns to
home screen.
†
CTL
F:Stop
Store: value!variable
Stores value in variable.
¿
StoreGDB n
Stores current graph in database
GDBn.
y <
STO
3:StoreGDB
StorePic n
Stores current picture in picture Picn. y <
STO
1:StorePic
String4Equ(string,Y= var) Converts string into an equation and
y N
String4Equ(
stores it in Y= var.
sub(string,begin,length)
Returns a string that is a subset of
another string, from begin to length.
y N
sub(
sum(list[,start,end])
Returns the sum of elements of list
from start to end.
y 9
MATH
5:sum(
tan(value)
Returns the tangent of a real
number, expression, or list.
š
L1
tan (value)
Returns the arctangent of a real
number, expression, or list.
y A
TI-83 Plus
Tables and Reference Information
686
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Tangent(expression,value) Draws a line tangent to expression at y <
X=value.
DRAW
5:Tangent(
tanh(value)
Returns hyperbolic tangent of a real
number, expression, or list.
y N
tanh(
L1
tanh (value)
Returns the hyperbolic arctangent of
a real number, expression, or list.
y N
tanh (
L1
tcdf(lowerbound,
upperbound,df)
Computes the Student-t distribution
y =
DISTR
probability between lowerbound and
upperbound for the specified degrees 5:tcdf(
of freedom df.
Text(row,column,text1,
text2,...,text n)
Writes text on graph beginning at
pixel (row,column), where
0 row 57 and 0 column 94.
y <
DRAW
0:Text(
Then
See If:Then
Time
Sets sequence graphs to plot with
respect to time.
† y .
Time
TInterval [listname,
freqlist,confidence level]
(Data list input)
Computes a t confidence interval.
† …
TESTS
8:TInterval
TInterval v,Sx,n
[,confidence level]
(Summary stats input)
Computes a t confidence interval.
† …
TESTS
8:TInterval
tpdf(x,df)
Computes the probability density
y =
DISTR
function (pdf) for the Student-t
distribution at a specified x value with 4:tpdf(
specified degrees of freedom df.
TI-83 Plus
Tables and Reference Information
687
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Trace
Displays the graph and enters
TRACE mode.
r
T-Test m0[,listname,
freqlist,alternative,
drawflag]
Performs a t test with frequency
freqlist. alternative=L1 is <;
† …
TESTS
2:T-Test
alternative=0 is ƒ; alternative=1 is >.
drawflag=1 draws results;
(Data list input)
drawflag=0 calculates results.
T-Test m0, v,Sx,n
[,alternative,drawflag]
(Summary stats input)
Performs a t test with frequency
freqlist. alternative=L1 is < ;
alternative=0 is ƒ ; alternative=1 is
>. drawflag=1 draws results;
drawflag=0 calculates results.
† …
TESTS
2:T-Test
tvm_FV[(Ú,æ,PV,PMT,
P/Y,C/Y)]
Computes the future value.
Π1:Finance
CALC
6:tvm_FV
tvm_æ[(Ú,PV,PMT,FV,
P/Y,C/Y)]
Computes the annual interest rate.
Π1:Finance
CALC
3:tvm_(
tvm_Ú[(æ,PV,PMT,FV,
P/Y,C/Y)]
Computes the number of payment
periods.
Π1:Finance
CALC
5:tvm_(
tvm_Pmt[(Ú,æ,PV,FV,
P/Y,C/Y)]
Computes the amount of each
payment.
Π1:Finance
CALC
2:tvm_Pmt
tvm_PV[(Ú,æ,PMT,FV,
P/Y,C/Y)]
Computes the present value.
Π1:Finance
CALC
4:tvm_PV
TI-83 Plus
Tables and Reference Information
688
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
UnArchive
Moves the specified variables from
the user data archive memory to
RAM.
y L
6:UnArchive
To archive variables, use Archive.
uvAxes
uwAxes
Sets sequence graphs to plot u(n) on † y .
the x-axis and v(n) on the y-axis. uv
Sets sequence graphs to plot u(n) on † y .
the x-axis and w(n) on the y-axis.
uw
1-Var Stats [Xlistname,
freqlist]
Performs one-variable analysis on
the data in Xlistname with frequency
freqlist.
…
CALC
1:1-Var Stats
2-Var Stats [Xlistname,
Ylistname,freqlist]
Performs two-variable analysis on
the data in Xlistname and Ylistname
with frequency freqlist.
…
CALC
2:2-Var Stats
variance(list[,freqlist])
Returns the variance of the elements y 9
in list with frequency freqlist.
MATH
8:variance(
Vertical x
Draws a vertical line at x.
y <
DRAW
4:Vertical
vwAxes
Web
Sets sequence graphs to plot v(n) on † y .
the x-axis and w(n) on the y-axis.
vw
Sets sequence graphs to trace as
webs.
† y .
Web
:While condition
:commands
:End
Executes commands while condition
is true.
†
CTL
5:While
:command
TI-83 Plus
Tables and Reference Information
689
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
valueA xor valueB
Returns 1 if only valueA or valueB =
0. valueA and valueB can be real
numbers, expressions, or lists.
y :
LOGIC
3:xor
ZBox
Displays a graph, lets you draw a box
that defines a new viewing window,
and updates the window.
† q
ZOOM
1:ZBox
ZDecimal
Adjusts the viewing window so that
@X=0.1 and @Y=0.1, and displays the
graph screen with the origin centered
on the screen.
† q
ZOOM
4:ZDecimal
ZInteger
Redefines the viewing window using
these dimensions:
† q
ZOOM
@X=1
@Y=1
Xscl=10
Yscl=10
8:ZInteger
ZInterval s[,listname,
freqlist,confidence level]
(Data list input)
Computes a z confidence interval.
† …
TESTS
7:ZInterval
ZInterval s,v,n
[,confidence level]
(Summary stats input)
Computes a z confidence interval.
† …
TESTS
7:ZInterval
Zoom In
Magnifies the part of the graph that
surrounds the cursor location.
† q
ZOOM
2:Zoom In
Zoom Out
Displays a greater portion of the
graph, centered on the cursor
location.
† q
ZOOM
3:Zoom Out
TI-83 Plus
Tables and Reference Information
690
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
ZoomFit
Recalculates Ymin and Ymax to
include the minimum and maximum
Y values, between Xmin and Xmax,
of the selected functions and replots
the functions.
† q
ZOOM
0:ZoomFit
ZoomRcl
ZoomStat
ZoomSto
ZPrevious
Graphs the selected functions in a
user-defined viewing window.
† q
MEMORY
3:ZoomRcl
Redefines the viewing window so
that all statistical data points are
displayed.
† q
ZOOM
9:ZoomStat
Immediately stores the current
viewing window.
† q
MEMORY
2:ZoomSto
Replots the graph using the window
variables of the graph that was
displayed before you executed the
last ZOOM instruction.
† q
MEMORY
1:ZPrevious
ZSquare
Adjusts the X or Y window settings
so that each pixel represents an
equal width and height in the
coordinate system, and updates the
viewing window.
† q
ZOOM
5:ZSquare
ZStandard
Replots the functions immediately,
updating the window variables to the
default values.
† q
ZOOM
6:ZStandard
TI-83 Plus
Tables and Reference Information
691
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
ZNTest(m0,s[,listname,
freqlist,alternative,
drawflag])
Performs a z test with frequency
freqlist. alternative=L1 is <;
† …
TESTS
1:Z.Test(
alternative=0 is ƒ; alternative=1 is >.
drawflag=1 draws results;
(Data list input)
drawflag=0 calculates results.
ZNTest(m0,s,v,n
[,alternative,drawflag])
(Summary stats input)
Performs a z test. alternative=L1 is <; † …
alternative=0 is ƒ; alternative=1 is >.
drawflag=1 draws results;
TESTS
1:Z.Test(
drawflag=0 calculates results.
ZTrig
Replots the functions immediately,
updating the window variables to
preset values for plotting trig
functions.
† q
ZOOM
7:ZTrig
Factorial: value!
Factorial: list!
Returns factorial of value.
PRB
4:!
Returns factorial of list elements.
PRB
4:!
Degrees notation: value¡
Radian: angler
Interprets value as degrees;
y ;
ANGLE
1:(
designates degrees in DMS format.
Interprets angle as radians.
y ;
ANGLE
r
3:
TI-83 Plus
Tables and Reference Information
692
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Transpose: matrixT
Returns a matrix in which each
element (row, column) is swapped
with the corresponding element
(column, row) of matrix.
y >
MATH
T
2:
xthrootx‡value
xthrootx‡list
listx‡value
Returns xthroot of value.
MATH
x
5: (
Returns xthroot of list elements.
Returns list roots of value.
Returns listA roots of listB.
MATH
x
5: (
MATH
x
5: (
listAx‡listB
Cube: value3
MATH
x
5: (
Returns the cube of a real or
complex number, expression, list, or
square matrix.
MATH
3
3:
3
Cube root: ‡(value)
Returns the cube root of a real or
complex number, expression, or list.
MATH
3
4: (
Equal: valueA=valueB
Returns 1 if valueA = valueB.
y :
Returns 0 if valueA ƒ valueB. valueA TEST
and valueB can be real or complex
numbers, expressions, lists, or
matrices.
1:=
TI-83 Plus
Tables and Reference Information
693
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Not equal: valueAƒvalueB Returns 1 if valueA ƒ valueB.
y :
Returns 0 if valueA = valueB. valueA TEST
and valueB can be real or complex
numbers, expressions, lists, or
matrices.
2:ƒ
Less than: valueA<valueB Returns 1 if valueA < valueB.
Returns 0 if valueA ‚ valueB. valueA
and valueB can be real or complex
y :
TEST
5:<
numbers, expressions, or lists.
Greater than:
valueA>valueB
Returns 1 if valueA > valueB.
y :
TEST
3:>
Returns 0 if valueA valueB. valueA
and valueB can be real or complex
numbers, expressions, or lists.
Less than or equal:
valueAvalueB
Returns 1 if valueA valueB.
y :
Returns 0 if valueA > valueB. valueA TEST
and valueB can be real or complex
numbers, expressions, or lists.
6:
Greater than or equal:
valueA‚valueB
Returns 1 if valueA ‚ valueB.
y :
Returns 0 if valueA < valueB. valueA TEST
and valueB can be real or complex
numbers, expressions, or lists.
4:‚
Inverse: valueL1
Returns 1 divided by a real or
complex number or expression.
œ
Inverse: listL1
Inverse: matrixL1
Square: value2
Returns 1 divided by list elements.
Returns matrix inverted.
Returns value multiplied by itself.
value can be a real or complex
number or expression.
œ
œ
¡
TI-83 Plus
Tables and Reference Information
694
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Square: list2
Square: matrix2
Powers: value^power
Returns list elements squared.
Returns matrix multiplied by itself.
Returns value raised to power. value
can be a real or complex number or
expression.
¡
¡
›
Powers: list^power
Returns list elements raised to
power.
›
Powers: value^list
Powers: matrix^power
Returns value raised to list elements.
Returns matrix elements raised to
power.
›
›
Negation: Lvalue
Returns the negative of a real or
complex number, expression, list, or
matrix.
Ì
Power of ten: 10^(value)
Returns 10 raised to the value
power. value can be a real or
complex number or expression.
y G
Power of ten: 10^(list)
Returns a list of 10 raised to the list
y G
y C
¯
power.
Square root: ‡(value)
Returns square root of a real or
complex number, expression, or list.
Multiplication:
valueAävalueB
Returns valueA times valueB.
Multiplication:
valueälist
Returns value times each list
element.
¯
Multiplication:
listävalue
Returns each list element times
value.
¯
TI-83 Plus
Tables and Reference Information
695
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Multiplication:
listAälistB
Multiplication:
valueämatrix
Multiplication:
matrixAämatrixB
Returns listA elements times listB
¯
¯
¯
elements.
Returns value times matrix
elements.
Returns matrixA times matrixB.
Division: valueAàvalueB
Division: listàvalue
Returns valueA divided by valueB.
Returns list elements divided by
value.
¥
¥
Division: valueàlist
Returns value divided by list
¥
¥
elements.
Division: listAàlistB
Returns listA elements divided by
listB elements.
Addition: valueA+valueB
Addition: list+value
Returns valueA plus valueB.
Returns list in which value is added
to each list element.
Ã
Ã
Addition: listA+listB
Returns listA elements plus listB
Ã
Ã
Ã
¹
¹
elements.
Addition:
matrixA+matrixB
Concatenation:
string1+string2
Subtraction:
valueANvalueB
Subtraction:
valueNlist
Returns matrixA elements plus
matrixB elements.
Concatenates two or more strings.
Subtracts valueB from valueA.
Subtracts list elements from value.
TI-83 Plus
Tables and Reference Information
696
Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Subtraction:
listNvalue
Subtraction:
listANlistB
Subtraction:
matrixANmatrixB
Subtracts value from list elements.
¹
¹
¹
Subtracts listB elements from listA
elements.
Subtracts matrixB elements from
matrixA elements.
Minutes notation:
degrees¡minutes'seconds" measurement as minutes.
Interprets minutes angle
y ;
ANGLE 2:'
Seconds notation:
degrees¡minutes'seconds" measurement as seconds.
Interprets seconds angle
ƒ [ã]
TI-83 Plus
Tables and Reference Information
697
TI-83 Plus Menu Map
The TI-83 Plus Menu Map begins at the top-left corner of the keyboard
and follows the keyboard layout from left to right. Default values and
settings are shown.
o
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func mode) (Par mode)
(Pol mode)
(Seq mode)
Plot1 Plot2 Plot1 Plot2 Plot1 Plot2 Plot1 Plot2
Plot3
çY1=
çY2=
çY3=
çY4=
...
Plot3
çX1T=
Y1T=
çX2T=
Y2T=
...
Plot3
çr1=
çr2=
çr3=
çr4=
çr5=
çr6=
Plot3
nMin=1
íu(n)=
u(nMin)=
ív(n)=
v(nMin)=
íw(n)=
w(nMin)=
çY9=
çY0=
çX6T=
Y6T=
y ,
y ,
ÚÄÄÄÄÄÙ
ÚÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
STAT PLOTS
1:Plot1…Off
" L1 L2 ›
2:Plot2…Off
" L1 L2 ›
3:Plot3…Off
" L1 L2 ›
4:PlotsOff
5:PlotsOn
(PRGM editor) (PRGM editor) (PRGM editor)
PLOTS
TYPE
MARK
1:›
2:+
3:¦
1:Plot1(
2:Plot2(
3:Plot3(
4:PlotsOff
5:PlotsOn
1:Scatter
2:xyLine
3:Histogram
4:ModBoxplot
5:Boxplot
6:NormProbPlot
TI-83 Plus
Tables and Reference Information
698
p
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func mode) (Par mode)
(Pol mode)
WINDOW
(Seq mode)
WINDOW
WINDOW
WINDOW
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
Tmin=0
qmin=0
nMin=1
Tmax=pä2
Tstep=pà24
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
qmax=pä2
qstep=pà24
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
nMax=10
PlotStart=1
PlotStep=1
Xmin=-10
Xmax=10
Xscl=1
Xres=1
Ymin=-10
Ymax=10
Yscl=1
y -
y -
ÚÄÄÄÙ
ÚÄÄÄÄÙ
TABLE SETUP
TblStart=0
(PRGM editor)
TABLE SETUP
@Tbl=1
Indpnt:Auto Ask
Depend:Auto Ask
Indpnt:Auto Ask
Depend:Auto Ask
TI-83 Plus
Tables and Reference Information
699
q
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ZOOM
MEMORY
MEMORY
1:ZBox
1:ZPrevious
2:ZoomSto
3:ZoomRcl
4:SetFactors…
(Set Factors...)
ZOOM FACTORS
XFact=4
2:Zoom In
3:Zoom Out
4:ZDecimal
5:ZSquare
6:ZStandard
7:ZTrig
YFact=4
8:ZInteger
9:ZoomStat
0:ZoomFit
y .
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func/Par/Pol modes) (Seq mode)
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Time Web uv vw uw
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
TI-83 Plus
Tables and Reference Information
700
y /
ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func mode) (Par mode)
(Pol mode)
CALCULATE
1:value
2:dy/dx
3:dr/dq
(Seq mode)
CALCULATE
1:value
CALCULATE
1:value
CALCULATE
1:value
2:dy/dx
3:dy/dt
4:dx/dt
2:zero
3:minimum
4:maximum
5:intersect
6:dy/dx
7:‰f(x)dx
z
ÚÙ
Normal Sci Eng
Float 0123456789
Radian Degree
Func Par Pol Seq
Connected Dot
Sequential Simul
Real a+b× re^q×
Full Horiz G-T
TI-83 Plus
Tables and Reference Information
701
y 8
ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
SEND
RECEIVE
1:All+…
1:Receive
2:AllN…
3:Prgm…
4:List…
5:Lists to TI82…
6:GDB…
7:Pic…
8:Matrix…
9:Real…
0:Complex…
A:Y-Vars…
B:String…
C:Apps…
D:AppVars…
E:Group…
F:SendId
G:SendOS
H:Back Up…
TI-83 Plus
Tables and Reference Information
702
…
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
EDIT
CALC
TESTS
1:Edit…
2:SortA(
3:SortD(
4:ClrList
5:SetUpEditor 5:QuadReg
6:CubicReg
1:1-Var Stats
2:2-Var Stats
3:Med-Med
1:Z-Test…
2:T-Test…
3:2-SampZTest…
4:2-SampTTest…
5:1-PropZTest…
6:2-PropZTest…
7:ZInterval…
8:TInterval…
9:2-SampZInt…
0:2-SampTInt…
A:1-PropZInt…
B:2-PropZInt…
C:c2-Test…
4:LinReg(ax+b)
7:QuartReg
8:LinReg(a+bx)
9:LnReg
0:ExpReg
A:PwrReg
B:Logistic
C:SinReg
D:2-SampÛTest…
E:LinRegTTest…
F:ANOVA(
TI-83 Plus
Tables and Reference Information
703
y 9
ÚÄÄÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
NAMES
OPS
MATH
1:listname 1:SortA(
2:listname 2:SortD(
3:listname 3:dim(
1:min(
2:max(
3:mean(
4:median(
5:sum(
...
4:Fill(
5:seq(
6:cumSum(
7:@List(
8:Select(
9:augment(
0:List4matr(
A:Matr4list(
B:Ù
6:prod(
7:stdDev(
8:variance(
ÚÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄ¿
MATH
NUM
CPX
PRB
1:4Frac
2:4Dec
3:3
1:abs(
2:round(
3:iPart(
4:fPart(
5:int(
6:min(
7:max(
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:4Rect
7:4Polar
1:rand
2:nPr
3:nCr
4:!
5:randInt(
6:randNorm(
7:randBin(
4:3‡(
x‡
5:
6:fMin(
7:fMax(
8:nDeriv( 8:lcm(
9:fnInt(
9:gcd(
0:Solver…
TI-83 Plus
Tables and Reference Information
704
y :
ÚÄÄÁÄÄÄÄÄÄÄÄÄ¿
TEST
1:=
2:ƒ
3:>
4:‚
5:<
6:
LOGIC
1:and
2:or
3:xor
4:not(
y >
y ;
ÚÁÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÚÄÄÄÙ
NAMES
1:[A]
2:[B]
3:[C]
4:[D]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
0:[J]
MATH
EDIT
ANGLE
1:¡
1:det(
1:[A]
2:[B]
3:[C]
4:[D]
2:T
2:'
r
3:dim(
4:Fill(
5:identity( 5:[E]
6:randM(
7:augment(
8:Matr4list( 8:[H]
9:List4matr( 9:[I]
0:cumSum(
A:ref(
3:
4:4DMS
5:R4Pr(
6:R4Pq(
7:P4Rx(
8:P4Ry(
6:[F]
7:[G]
0:[J]
B:rref(
C:rowSwap(
D:row+(
E:…row(
F:…row+(
TI-83 Plus
Tables and Reference Information
705
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
EXEC
EDIT
NEW
1:name
2:name
...
1:name
2:name
...
1:Create New
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(PRGM editor) (PRGM editor) (PRGM editor)
CTL
I/O
EXEC
1:If
1:Input
2:Prompt
3:Disp
1:name
2:name
...
2:Then
3:Else
4:For(
5:While
6:Repeat
7:End
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHome
9:ClrTable
0:GetCalc(
A:Get(
8:Pause
9:Lbl
0:Goto
A:IS>(
B:DS<(
C:Menu(
D:prgm
E:Return
F:Stop
G:DelVar
H:GraphStyle(
B:Send(
TI-83 Plus
Tables and Reference Information
706
y <
ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
DRAW
POINTS
STO
1:ClrDraw
2:Line(
1:Pt-On(
2:Pt-Off(
1:StorePic
2:RecallPic
3:Horizontal 3:Pt-Change( 3:StoreGDB
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:DrawInv
9:Circle(
0:Text(
4:Pxl-On(
4:RecallGDB
5:Pxl-Off(
6:Pxl-Change(
7:pxl-Test(
A:Pen
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
VARS
Y-VARS
1:Window…
2:Zoom…
3:GDB…
1:Function…
2:Parametric…
3:Polar…
4:Picture…
5:Statistics…
6:Table…
7:String…
4:On/Off…
TI-83 Plus
Tables and Reference Information
707
VARS
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂ
(Window…) (Window…) (Window…)
X/Y
T/q
U/V/W
1:Xmin
2:Xmax
3:Xscl
4:Ymin
5:Ymax
6:Yscl
7:Xres
8:@X
1:Tmin
2:Tmax
3:Tstep
4:qmin
5:qmax
6:qstep
1:u(nMin)
2:v(nMin)
3:w(nMin)
4:nMin
5:nMax
6:PlotStart
7:PlotStep
9:@Y
0:XFact
A:YFact
VARS
ÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄ
(Zoom…)
ZX/ZY
(Zoom…)
ZT/Zq
(Zoom…)
ZU
1:ZXmin
2:ZXmax
3:ZXscl
4:ZYmin
5:ZYmax
6:ZYscl
7:ZXres
1:ZTmin
2:ZTmax
3:ZTstep 3:Zw(nMin)
4:Zqmin
5:Zqmax
6:Zqstep 6:ZPlotStart
1:Zu(nMin)
2:Zv(nMin)
4:ZnMin
5:ZnMax
7:ZPlotStep
TI-83 Plus
Tables and Reference Information
708
VARS
ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ
(GDB…)
(Picture…
GRAPH DATABASE )
1:GDB1
2:GDB2
...
9:GDB9
0:GDB0
PICTURE
1:Pic1
2:Pic2
...
9:Pic9
0:Pic0
TI-83 Plus
Tables and Reference Information
709
VARS
ÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄ
(Statistics…) (Statistics…) (Statistics…) (Statistics…) (Statistics…)
XY
1:n
2:v
G
EQ
1:RegEQ
2:a
3:b
4:c
TEST
1:p
2:z
PTS
1:Gx
2:Gx2
3:Gy
4:Gy2
5:Gxy
1:x1
2:y1
3:x2
4:y2
5:x3
6:y3
7:Q1
8:Med
9:Q3
3:Sx
4:sx
5:w
6:Sy
7:sy
8:minX
9:maxX
0:minY
A:maxY
3:t
4:c2
5:Û
5:d
6:e
6:df
7:Ç
8:Ç1
9:Ç2
0:s
A:ü1
B:ü2
C:Sx1
D:Sx2
E:Sxp
F:n1
G:n2
H:lower
I:upper
7:r
8:r2
9:R2
TI-83 Plus
Tables and Reference Information
710
VARS
ÄÂÄÄÄÄÄÄÄÄÄÄÄ¿
(Table…)
TABLE
1:TblStart
2:@Tbl
(String…)
STRING
1:Str1
2:Str2
3:Str3
4:Str4
...
3:TblInput
9:Str9
0:Str0
Y-VARS
ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿
(Function…) (Parametric…)(Polar…) (On/Off…)
FUNCTION
1:Y1
2:Y2
3:Y3
4:Y4
PARAMETRIC
1:X1T
2:Y1T
3:X2T
4:Y2T
POLAR
1:r1
2:r2
3:r3
4:r4
5:r5
6:r6
ON/OFF
1:FnOn
2:FnOff
...
9:Y9
...
A:X6T
0:Y0
B:Y6T
TI-83 Plus
Tables and Reference Information
711
y =
ÚÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
DISTR
DRAW
1:normalpdf(
2:normalcdf(
3:invNorm(
4:tpdf(
1:ShadeNorm(
2:Shade_t(
3:Shadec2(
4:ShadeÛ(
5:tcdf(
6:c2pdf(
7:c2cdf(
8:Ûpdf(
9:Ûcdf(
0:binompdf(
A:binomcdf(
B:poissonpdf(
C:poissoncdf(
D:geometpdf(
E:geometcdf(
TI-83 Plus
Tables and Reference Information
712
Œ
ÚÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄ¿
1:Finance
2:CBL/CBR
Finance
ÚÄÄÄÄÄÁÄÄÄÄÄ¿
CBL/CBR
ÚÄÄÄÙ
CALC
1:TVM
Solver…
VARS
1:Ú
2:æ
1:GAUGE
2:DATA LOGGER
3:CBR
2:tvm_Pmt 3:PV
4:QUIT
3:tvm_æ
4:tvm_PV
5:tvm_Ú
6:tvm_FV
7:npv(
4:PMT
5:FV
6:P/Y
7:C/Y
8:irr(
9:bal(
0:GPrn(
A:GInt(
B:4Nom(
C:4Eff(
D:dbd(
E:Pmt_End
F:Pmt_Bgn
TI-83 Plus
Tables and Reference Information
713
y L
ÚÄÄÙ
MEMORY
ÚÄÄÙ
MEMORY
1:About
(Mem Mgmt/Del…)
RAM FREE 25631
2:Mem Mgmt/Del… ARC FREE 131069
3:Clear Entries 1:All…
4:ClrAllLists 2:Real…
5:Archive
6:UnArchive
7:Reset…
8:Group
3:Complex…
4:List…
5:Matrix…
6:Y-Vars…
7:Prgm…
8:Pic…
9:GDB…
0:String…
A:Apps…
B:AppVars…
C:Group…
TI-83 Plus
Tables and Reference Information
714
MEMORY (Reset…)
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
RAM
1:All RAM…
2:Defaults…
ARCHIVE
1:Vars…
2:Apps…
B:Both…
ALL
1:All Memory…
Resetting RAM
Resetting Both
Resetting ALL
erases all data
erases all data,
erases all data,
and programs from programs and Apps programs and Apps
RAM.
from Archive.
from RAM and
Archive.
RAM
ÚÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄ¿
RESET RAM
1:No
RESET DEFAULTS
1:No
2:Reset
2:Reset
Resetting RAM
erases all data
and programs from
RAM.
TI-83 Plus
Tables and Reference Information
715
ARCHIVE
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
RESET ARC VARS
1:No
RESET ARC APPS
1:No
RESET ARC BOTH
1:No
2:Reset
2:Reset
2:Reset
Resetting Vars
erases all data
and programs from from Archive.
Archive.
Resetting Apps
erases all Apps
Resetting Both
erases all data,
programs and Apps
from Archive.
ALL
ÚÄÄÙ
RESET MEMORY
1:No
2:Reset
Resetting ALL
will delete all
data, programs &
Apps from RAM &
Archive.
MEMORY (GROUP...)
ÚÄÄÁÄÄ¿
GROUP UNGROUP
1:Create New
TI-83 Plus
Tables and Reference Information
716
MEMORY
(UNGROUP...)
ÚÄÄÙ
1:name
2:name
...
y N
ÚÄÄÙ
CATALOG
cosh(
coshL1(
...
Equ4String(
expr(
...
inString(
...
length(
...
sinh(
sinhL1(
...
String4Equ(
sub(
...
tanh(
tanhL1(
TI-83 Plus
Tables and Reference Information
717
Variables
User Variables
The TI-83 Plus uses the variables listed below in various ways. Some
variables are restricted to specific data types.
The variables A through Z and q are defined as real or complex
numbers. You may store to them. The TI-83 Plus can update X, Y, R, q,
and T during graphing, so you may want to avoid using these variables
to store nongraphing data.
The variables (list names) L1 through L6 are restricted to lists; you
cannot store another type of data to them.
The variables (matrix names) [A] through [J] are restricted to matrices;
you cannot store another type of data to them.
The variables Pic1 through Pic9 and Pic0 are restricted to pictures; you
cannot store another type of data to them.
The variables GDB1 through GDB9 and GDB0 are restricted to graph
databases; you cannot store another type of data to them.
The variables Str1 through Str9 and Str0 are restricted to strings; you
cannot store another type of data to them.
TI-83 Plus
Tables and Reference Information
718
Except for system variables, you can store any string of characters,
functions, instructions, or variables to the functions Yn, (1 through 9, and
0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n), and w(n) directly or
through the Y= editor. The validity of the string is determined when the
function is evaluated.
Archive Variables
You can store data, programs or any variable from RAM to user data
archive memory where they cannot be edited or deleted inadvertantly.
Archiving also allows you to free up RAM for variables that may require
additional memory. The names of archived variables are preceded by an
asterisk “*” indicating they are in user data archive.
System Variables
The variables below must be real numbers. You may store to them.
Since the TI-83 Plus can update some of them, as the result of a ZOOM,
for example, you may want to avoid using these variables to store
nongraphing data.
• Xmin, Xmax, Xscl, @X, XFact, Tstep, PlotStart, nMin, and other
window variables.
• ZXmin, ZXmax, ZXscl, ZTstep, ZPlotStart, Zu(nMin), and other
ZOOM variables.
TI-83 Plus
Tables and Reference Information
719
The variables below are reserved for use by the TI-83 Plus. You cannot
store to them.
n, v, Sx, sx, minX, maxX, Gy, Gy2, Gxy, a, b, c, RegEQ, x1, x2, y1, z, t,
F, c2, Ç, v1, Sx1, n1, lower, upper, r2, R2 and other statistical variables.
TI-83 Plus
Tables and Reference Information
720
Statistics Formulas
This section contains statistics formulas for the Logistic and SinReg
regressions, ANOVA, 2.SampÜTest, and 2.SampTTest.
Logistic
The logistic regression algorithm applies nonlinear recursive least-
squares techniques to optimize the following cost function:
J = N
− yi
c
2
∑
1+ ae − bx
i
i=1
which is the sum of the squares of the residual errors,
where:
x = the independent variable list
y = the dependent variable list
N = the dimension of the lists
This technique attempts to estimate the constants a, b, and c recursively
to make J as small as possible.
TI-83 Plus
Tables and Reference Information
721
SinReg
The sine regression algorithm applies nonlinear recursive least-squares
techniques to optimize the following cost function:
N
2
[
a
sin(
bxi + c + d − yi
]
)
J =
∑
i=1
which is the sum of the squares of the residual errors,
where:
x = the independent variable list
y = the dependent variable list
N = the dimension of the lists
This technique attempts to recursively estimate the constants a, b, c, and
d to make J as small as possible.
ANOVA(
The ANOVA Û statistic is:
FactorMS
Û =
ErrorMS
TI-83 Plus
Tables and Reference Information
722
The mean squares (MS) that make up Û are:
FactorSS
Factor MS =
Factordf
ErrorSS
Error MS =
Errordf
The sum of squares (SS) that make up the mean squares are:
I
Factor SS = ni(xi − x)2
∑
i=1
I
Error SS = (ni −1)Sxi2
∑
i=1
The degrees of freedom df that make up the mean squares are:
Factordf = I −1 = numeratordf for Û
I
Error df = (ni −1) = denominatordf for Û
∑
i=1
TI-83 Plus
Tables and Reference Information
723
where:
I = number of populations
xi = the mean of each list
Sxi = the standard deviation of each list
ni = the length of each list
x = the mean of all lists
2.SampÜTest
Below is the definition for the 2.SampÜTest.
Sx1, Sx2 = Sample standard deviations having n1-1 and n2-1
degrees of freedom df, respectively.
2
Sx1
Û = Û-statistic =
Sx2
df(x, n1-1, n2-1) = Ûpdf( ) with degrees of freedom df, n1-1, and n2-1
p = reported p value
TI-83 Plus
Tables and Reference Information
724
2.SampÜTest for the alternative hypothesis s1 > s2.
∞
p = f (x,n1 −1,n2 −1)dx
∫
F
2.SampÜTest for the alternative hypothesis s1 < s2.
F
p = f (x,n1 −1,n2 −1)dx
∫
0
2.SampÜTest for the alternative hypothesis s1 ƒ s2. Limits must satisfy
the following:
Lbnd
∞
p
=
f (x,n1 −1,n2 −1)dx = f (x,n1 −1,n2 −1)dx
∫
∫
2
0
Ubnd
where: [Lbnd,Ubnd] = lower and upper limits
The Û-statistic is used as the bound producing the smallest integral. The
remaining bound is selected to achieve the preceding integral’s equality
relationship.
TI-83 Plus
Tables and Reference Information
725
2.SampTTest
The following is the definition for the 2.SampTTest. The two-sample t
statistic with degrees of freedom df is:
x1 − x2
t =
S
where the computation of S and df are dependent on whether the
variances are pooled. If the variances are not pooled:
2
2
Sx1
n1
Sx2
n2
S =
+
2
2
2
Sx1 Sx2
+
n1
n2
df =
2
2
2
2
1
Sx1
1
Sx2
+
n1 −1 n1
n2 −1 n2
TI-83 Plus
Tables and Reference Information
726
otherwise:
2
2
(n1 −1)Sx1 + (n2 −1)Sx2
Sxp =
df
1
1
S =
+
Sxp
n1 n2
df = n1 + n2 − 2
and Sxp is the pooled variance.
TI-83 Plus
Tables and Reference Information
727
Financial Formulas
This section contains financial formulas for computing time value of
money, amortization, cash flow, interest-rate conversions, and days
between dates.
Time Value of Money
i = [e( y × ln(x + 1))]−1
where: PMT ƒ 0
y = C/Y ÷ P/Y
x = (.01 × I%) ÷ C/Y
C/Y = compounding periods per year
P/Y = payment periods per year
I% = interest rate per year
i = (−FV ÷ PV )(1 ÷ N ) −1
where: PMT = 0
The iteration used to compute i:
1− (1+ i) −
N
+ FV ×(1+ i) −
N
0 = PV + PMT ×Gi
i
TI-83 Plus
Tables and Reference Information
728
I% =100 ×C/Y ×[e( y × ln(x +1)) −1]
where:
x = i
y = P/Y ÷ C/Y
Gi = 1+ i × k
where:
k = 0 for end-of-period payments
k = 1 for beginning-of-period payments
PMT ×Gi − FV ×i
PMT ×Gi + PV ×i
ln(1+ i)
ln
N =
where:
i ƒ 0
N = −(PV + FV ) ÷ PMT
where:
i = 0
PMT = − × PV +
i
PV + FV
(1+ i)N −1
Gi
TI-83 Plus
Tables and Reference Information
729
where:
i ƒ 0
PMT = −(PV + FV ) ÷ N
where:
i = 0
PMT ×G
1
PMT ×Gi
PV =
where:
i − FV ×
−
i
(1+ i)N
i
i ƒ 0
PV = −(FV + PMT × N)
where:
i = 0
PMT ×Gi
PMT ×Gi
FV =
where:
− (1+ i)N × PV +
i
i
i ƒ 0
FV = −(PV + PMT × N)
where: i = 0
TI-83 Plus
Tables and Reference Information
730
Amortization
If computing bal(), pmt2 = npmt
Let bal(0) = RND(PV)
Iterate from m = 1 to pmt2
−
Im = RND[RND12( i ×bal(m −1))]
bal(m) = bal(m −1) − Im+ RND(PMT )
then:
bal() = bal( pmt2)
Σ Prn() = bal( pmt2) − bal( pmt1)
ΣInt() = ( pmt2 − pmt1+1) × RND(PMT ) − Σ Prn()
TI-83 Plus
Tables and Reference Information
731
where:
RND = round the display to the number of decimal places
selected
RND12 = round to 12 decimal places
Balance, principal, and interest are dependent on the values of PMT, PV,
æ, and pmt1 and pmt2.
Cash Flow
N
Sj − 1 (1− (1+ i)−
)
nj
npv() = CF0 + CFj(1+ i) −
∑
i
j=1
j
ni j ≥1
∑
where:
Sj =
i=1
0
j = 0
Net present value is dependent on the values of the initial cash flow
(CF0), subsequent cash flows (CFj), frequency of each cash flow (nj),
and the specified interest rate (i).
irr() = 100 × i, where i satisfies npv() = 0
TI-83 Plus
Tables and Reference Information
732
Internal rate of return is dependent on the values of the initial cash flow
(CF0) and subsequent cash flows (CFj).
i =I% ÷ 100
Interest Rate Conversions
4Eff = 100×(eCP × ln(x + 1) −1)
where:
where:
x = .01 × Nom ÷ CP
4Nom = 100×CP ×[e1 ÷ CP × ln(x + 1) −1]
x = .01 × Eff
Eff = effective rate
CP = compounding periods
Nom = nominal rate
Days between Dates
With the dbd( function, you can enter or compute a date within the
range Jan. 1, 1950, through Dec. 31, 2049.
TI-83 Plus
Tables and Reference Information
733
Actual/actual day-count method (assumes actual number of days per
month and actual number of days per year):
dbd( (days between dates) = Number of Days II - Number of Days I
Number of Days I = (Y1-YB) × 365
+ (number of days MB to M1)
+ DT1
(Y1−YB)
+
4
Number of Days II = (Y2-YB) × 365
+ (number of days MB to M2)
+ DT2
(Y 2 −YB)
+
4
where:
M1 = month of first date
DT1 = day of first date
Y1 = year of first date
M2 = month of second date
DT2 = day of second date
Y2 = year of second date
MB = base month (January)
DB = base day (1)
YB = base year (first year after leap year)
TI-83 Plus
Tables and Reference Information
734
Appendix B:
General Information
Battery Information
When to Replace the Batteries
The TI-83 Plus uses five batteries: four AAA alkaline batteries and one
lithium battery. The lithium battery provides auxiliary power to retain
memory while you replace the AAA batteries.
When the battery voltage level drops below a usable level, the TI-83 Plus:
Displays this message when
you turn on the unit.
Displays this message when you
attempt to download an application.
Message A
Message B
TI-83 Plus
General Information
735
After Message A is first displayed, you can expect the batteries to
function for about one or two weeks, depending on usage. (This one-
week to two-week period is based on tests with alkaline batteries; the
performance of other kinds of batteries may vary.)
The low-battery message continues to be displayed each time you turn
on the unit until you replace the batteries. If you do not replace the
batteries within about two weeks, the calculator may turn off by itself or
fail to turn on until you install new batteries.
If Message B is displayed, you must to replace the batteries immediately
to successfully download an application.
Replace the lithium battery every three or four years.
Effects of Replacing the Batteries
Do not remove both types of batteries (AAA and lithium auxiliary) at the
same time. Do not allow the batteries to lose power completely. If you
follow these guidelines and the steps for replacing batteries, you can
replace either type of battery without losing any information in memory.
TI-83 Plus
General Information
736
Battery Precautions
Take these precautions when replacing batteries.
• Do not leave batteries within reach of children
• Do not mix new and used batteries. Do not mix brands (or types
within brands) of batteries.
• Do not mix rechargeable and nonrechargeable batteries.
• Install batteries according to polarity (+ and N) diagrams.
• Do not place nonrechargeable batteries in a battery recharger.
• Properly dispose of used batteries immediately. Do not leave them
within the reach of children.
• Do not incinerate or dismantle batteries.
Replacing the Batteries
To replace the batteries, follow these steps.
1. Turn off the calculator. Replace the slide cover over the keyboard to
avoid inadvertently turning on the calculator. Turn the back of the
calculator toward you.
2. Hold the calculator upright, push downward on the latch on the top of
the battery cover with your finger, and then pull the cover toward you.
TI-83 Plus
General Information
737
Note: To avoid loss of information stored in memory, you must turn off the
calculator. Do not remove the AAA batteries and the lithium battery
simultaneously.
3. Replace all four AAA alkaline batteries simultaneously. Or, replace
the lithium battery.
• To replace the AAA alkaline batteries, remove all four discharged
AAA batteries and install new ones according to the polarity
(+ and N) diagram in the battery compartment.
• To replace the lithium battery, remove the screw from the lithium-
battery cover, and then remove the cover. Install the new battery,
+ side up. Replace the cover and secure it with the screw. Use a
CR1616 or CR1620 (or equivalent) lithium battery.
4. Replace the battery compartment cover. Turn the calculator on and
adjust the display contrast, if necessary.
TI-83 Plus
General Information
738
In Case of Difficulty
Handling a Difficulty
To handle a difficulty, follow these steps.
1. If you cannot see anything on the screen, the contrast may need to
be adjusted.
To darken the screen, press and release y, and then press and
hold } until the display is sufficiently dark.
To lighten the screen, press and release y, and then press and
hold † until the display is sufficiently light.
2. If an error menu is displayed, follow the steps in Chapter 1. Refer to
necessary.
3. If the busy indicator (dotted line) is displayed, a graph or program has
been paused; the TI-83 Plus is waiting for input. Press Í to
continue or press É to break.
4. If a checkerboard cursor ( # ) is displayed, then either you have
entered the maximum number of characters in a prompt, or memory
is full. If memory is full:
TI-83 Plus
General Information
739
• Press y L 2 to display the MEMORY MANAGEMENT DELETE menu.
• Select the type of data you want to delete, or select 1:All for a list
of all variables of all types. A screen is displayed listing each
variable of the type you selected and the number of bytes each
variable is using.
• Press } and † to move the selection cursor (4) next to the item
you want to delete, and then press {. (Chapter 18).
5. If the calculator does not seem to work at all, be sure the batteries
are fresh and that they are installed properly. Refer to battery
information on pages 736 and 737.
6. If the calculator still doesn’t work even though you are sure the
batteries are sufficiently charged, you can try the two solutions in the
order they are presented.
• Download calculator system software as follows:
a. Remove one battery from the calculator and then press and
hold the { key while re-installing the battery. This will force
the calculator to accept a download of system software.
b. Connect your calculator to a personal computer with the
TI.GRAPH LINK™ accessory to download current or
new software code to your calculator.
TI-83 Plus
General Information
740
• II. If the above solution does not work, reset all memory as
follows:
a. Remove one battery from the calculator and then press and
hold down the ‘ key while re-installing the battery. While
continuing to hold down the ‘ key, press and hold down
the É key. When the home screen is displayed, release the
keys.
b. Press y L to display the MEMORY menu.
c. Select 7:Reset to display the RAM ARCHIVE ALL menu.
d. Press ~ ~ to display the ALL menu.
e. Select 1:All Memory to display the RESET MEMORY menu.
f. To continue with the reset, select 2:Reset. The message MEM
cleared is displayed on the home screen.
TI-83 Plus
General Information
741
Error Conditions
When the TI-83 Plus detects an error, it displays ERR:message and an
error menu. Chapter 1 describes the general steps for correcting errors.
This table contains each error type, possible causes, and suggestions for
correction.
Error Type
ARCHIVED
Possible Causes and Suggested Remedies
You have attempted to use, edit, or delete an archived
variable. For example, dim(L1) is an error if L1 is archived.
ARCHIVE FULL
ARGUMENT
You have attempted to archive a variable and there is not
enough space in archive to receive it.
A function or instruction does not have the correct number
of arguments. See Appendix A and the appropriate
chapter.
BAD ADDRESS
You have attempted to send or receive an application and
an error (e.g. electrical interference) has occurred in the
transmission.
TI-83 Plus
General Information
742
Error Type
Possible Causes and Suggested Remedies
BAD GUESS
• In a CALC operation, you specified a Guess that is not
between Left Bound and Right Bound.
• For the solve( function or the equation solver, you
specified a guess that is not between lower and upper.
• Your guess and several points around it are undefined.
Examine a graph of the function. If the equation has a
solution, change the bounds and/or the initial guess.
BOUND
BREAK
• In a CALC operation or with Select(, you defined
Left Bound > Right Bound.
• In fMin(, fMax(, solve(, or the equation solver, you
entered lower ‚ upper.
You pressed the É key to break execution of a program,
to halt a DRAW instruction, or to stop evaluation of an
expression.
TI-83 Plus
General Information
743
Error Type
Possible Causes and Suggested Remedies
DATA TYPE
You entered a value or variable that is the wrong data
type.
• For a function (including implied multiplication) or an
instruction, you entered an argument that is an invalid
data type, such as a complex number where a real
number is required. See Appendix A and the
appropriate chapter.
• In an editor, you entered a type that is not allowed, such
as a matrix entered as an element in the stat list editor.
See the appropriate chapter.
• You attempted to store an incorrect data type, such as a
matrix, to a list.
DIM MISMATCH
DIVIDE BY 0
You attempted to perform an operation that
references more than one list or matrix, but the
dimensions do not match.
• You attempted to divide by zero. This error is not
returned during graphing. The TI-83 Plus allows for
undefined values on a graph.
• You attempted a linear regression with a vertical line.
TI-83 Plus
General Information
744
Error Type
DOMAIN
Possible Causes and Suggested Remedies
• You specified an argument to a function or instruction
outside the valid range. This error is not returned during
graphing. The TI-83 Plus allows for undefined values on
a graph. See Appendix A and the appropriate chapter.
• You attempted a logarithmic or power regression with a
LX or an exponential or power regression with a LY.
• You attempted to compute GPrn( or GInt( with
pmt2 < pmt1.
DUPLICATE
• You attempted to create a duplicate group name.
Duplicate Name
• A variable you attempted to transmit cannot be
transmitted because a variable with that name already
exists in the receiving unit.
EXPIRED
You have attempted to run an application with a limited
trial period which has expired.
TI-83 Plus
General Information
745
Error Type
Possible Causes and Suggested Remedies
Error in Xmit
• The TI-83 Plus was unable to transmit an item. Check
to see that the cable is firmly connected to both units
and that the receiving unit is in receive mode.
• You pressed É to break during transmission.
• You attempted to perform a backup from a TI.82 to a
TI-83 Plus.
• You attempted to transfer data (other than L1 through
L6) from a TI-83 Plus to a TI.82.
• You attempted to transfer L1 through L6 from a
TI-83 Plus to a TI.82 without using 5:Lists to TI82 on
the LINK SEND menu.
ID NOT FOUND
ILLEGAL NEST
INCREMENT
This error occurs when the SendID command is executed
but the proper calculator ID cannot be found.
• You attempted to use an invalid function in an argument
to a function, such as seq( within expression for seq(.
• The increment in seq( is 0 or has the wrong sign. This
error is not returned during graphing. The TI-83 Plus
allows for undefined values on a graph.
• The increment in a For( loop is 0.
TI-83 Plus
General Information
746
Error Type
INVALID
Possible Causes and Suggested Remedies
• You attempted to reference a variable or use a function
where it is not valid. For example, Yn cannot reference
Y, Xmin, @X, or TblStart.
• You attempted to reference a variable or function that
was transferred from the TI.82 and is not valid for the
TI-83 Plus. For example, you may have transferred
UnN1 to the TI-83 Plus from the TI.82 and then tried to
reference it.
• In Seq mode, you attempted to graph a phase plot
without defining both equations of the phase plot.
• In Seq mode, you attempted to graph a recursive
sequence without having input the correct number of
initial conditions.
• In Seq mode, you attempted to reference terms other
than (nN1) or (nN2).
• You attempted to designate a graph style that is invalid
within the current graph mode.
• You attempted to use Select( without having selected
(turned on) at least one xyLine or scatter plot.
TI-83 Plus
General Information
747
Error Type
Possible Causes and Suggested Remedies
• You specified dimensions for an argument that are not
INVALID DIM
appropriate for the operation.
• You specified a list dimension as something other than
an integer between 1 and 999.
• You specified a matrix dimension as something other
than an integer between 1 and 99.
• You attempted to invert a matrix that is not square.
• The solve( function or the equation solver has
exceeded the maximum number of permitted iterations.
Examine a graph of the function. If the equation has a
solution, change the bounds, or the initial guess, or
both.
ITERATIONS
• irr( has exceeded the maximum number of permitted
iterations.
• When computing æ, the maximum number of iterations
was exceeded.
The label in the Goto instruction is not defined with a Lbl
instruction in the program.
LABEL
TI-83 Plus
General Information
748
Error Type
MEMORY
Possible Causes and Suggested Remedies
Memory is insufficient to perform the instruction or
function. You must delete items from memory (Chapter 18)
before executing the instruction or function.
Recursive problems return this error; for example,
graphing the equation Y1=Y1.
Branching out of an If/Then, For(, While, or Repeat loop
with a Goto also can return this error because the End
statement that terminates the loop is never reached.
• You are unable to transmit an item because the
receiving unit’s available memory is insufficient. You
may skip the item or exit receive mode.
MemoryFull
• During a memory backup, the receiving unit’s available
memory is insufficient to receive all items in the sending
unit’s memory. A message indicates the number of
bytes the sending unit must delete to do the memory
backup. Delete items and try again.
You attempted to store to a window variable in another
graphing mode or to perform an instruction while in the
wrong mode; for example, DrawInv in a graphing mode
other than Func.
MODE
TI-83 Plus
General Information
749
Error Type
Possible Causes and Suggested Remedies
• The solve( function or the equation solver did not
NO SIGN CHNG
detect a sign change.
• You attempted to compute æ when FV, (ÚäPMT), and
PV are all ‚ 0, or when FV, (ÚäPMT), and PV are all
0.
• You attempted to compute irr( when neither CFList nor
CFO is > 0, or when neither CFList nor CFO is < 0.
In Real mode, the result of a calculation yielded a complex
result. This error is not returned during graphing. The
TI-83 Plus allows for undefined values on a graph.
NONREAL ANS
OVERFLOW
You attempted to enter, or you have calculated, a number
that is beyond the range of the calculator. This error is not
returned during graphing. The TI-83 Plus allows for
undefined values on a graph.
You attempted to use a system variable inappropriately.
See Appendix A.
RESERVED
• A singular matrix (determinant = 0) is not valid as the
SINGULAR MAT
argument for L1.
• The SinReg instruction or a polynomial regression
generated a singular matrix (determinant = 0) because
it could not find a solution, or a solution does not exist.
This error is not returned during graphing. The TI-83 Plus
allows for undefined values on a graph.
TI-83 Plus
General Information
750
Error Type
Possible Causes and Suggested Remedies
expression in the solve( function or the equation solver
contains a singularity (a point at which the function is not
defined). Examine a graph of the function. If the equation
has a solution, change the bounds or the initial guess or
both.
SINGULARITY
You attempted a stat calculation with lists that are not
appropriate.
STAT
• Statistical analyses must have at least two data points.
• Med.Med must have at least three points in each
partition.
• When you use a frequency list, its elements must be
‚ 0.
• (Xmax N Xmin) à Xscl must be 47 for a histogram.
You attempted to display a graph when a stat plot that
uses an undefined list is turned on.
STAT PLOT
SYNTAX
The command contains a syntax error. Look for misplaced
functions, arguments, parentheses, or commas. See
Appendix A and the appropriate chapter.
You requested a tolerance to which the algorithm cannot
return an accurate result.
TOL NOT MET
TI-83 Plus
General Information
751
Error Type
Possible Causes and Suggested Remedies
You referenced a variable that is not currently defined. For
example, you referenced a stat variable when there is no
current calculation because a list has been edited, or you
referenced a variable when the variable is not valid for the
current calculation, such as a after Med.Med.
UNDEFINED
Electrical interference caused a link to fail or this calculator
is not authorized to run the application.
VALIDATION
VARIABLE
You have tried to archive a variable that cannot be
archived or you have have.tried to unarchive an application
or group.
Examples of variables that cannot be archived include:
• Real numbers LRESID, R, T, X, Y, Theta, Statistic
variables under Vars, STATISTICS menu, Yvars, and
the AppIdList.
You have attempted to receive an incompatible variable
version from another calculator.
VERSION
TI-83 Plus
General Information
752
Error Type
Possible Causes and Suggested Remedies
A problem exists with the window variables.
• You defined Xmax Xmin or Ymax Ymin.
WINDOW RANGE
• You defined qmax qmin and qstep > 0 (or vice
versa).
• You attempted to define Tstep=0.
• You defined Tmax Tmin and Tstep > 0 (or vice
versa).
• Window variables are too small or too large to graph
correctly. You may have attempted to zoom in or zoom
out to a point that exceeds the TI-83 Plus’s numerical
range.
• A point or a line, instead of a box, is defined in ZBox.
ZOOM
• A ZOOM operation returned a math error.
TI-83 Plus
General Information
753
Accuracy Information
Computational Accuracy
To maximize accuracy, the TI-83 Plus carries more digits internally than
it displays. Values are stored in memory using up to 14 digits with a two-
digit exponent.
• You can store a value in the window variables using up to 10 digits
(12 for Xscl, Yscl, Tstep, and qstep).
• Displayed values are rounded as specified by the mode setting with a
maximum of 10 digits and a two-digit exponent.
•
RegEQ displays up to 14 digits in Float mode. Using a fixed-decimal
setting other than Float causes RegEQ results to be rounded and
stored with the specified number of decimal places.
Xmin is the center of the leftmost pixel, Xmax is the center of the next-to-
the-rightmost pixel. (The rightmost pixel is reserved for the busy
indicator.) @X is the distance between the centers of two adjacent pixels.
• In Full screen mode, @X is calculated as (Xmax N Xmin) à 94. In G.T
split-screen mode, @X is calculated as (Xmax N Xmin) à 46.
• If you enter a value for @X from the home screen or a program in Full
screen mode, Xmax is calculated as Xmin + @X … 94. In G.T split-
screen mode, Xmax is calculated as Xmin + @X … 46.
TI-83 Plus
General Information
754
Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of
the top pixel. @Y is the distance between the centers of two adjacent
pixels.
• In Full screen mode, @Y is calculated as (Ymax N Ymin) à 62. In Horiz
split-screen mode, @Y is calculated as (Ymax N Ymin) à 30. In G.T
split-screen mode, @Y is calculated as (Ymax N Ymin) à 50.
• If you enter a value for @Y from the home screen or a program in Full
screen mode, Ymax is calculated as Ymin + @Y … 62. In Horiz split-
screen mode, Ymax is calculated as Ymin + @Y … 30. In G.T split-
screen mode, Ymax is calculated as Ymin + @Y … 50.
Cursor coordinates are displayed as eight-character numbers (which
may include a negative sign, decimal point, and exponent) when Float
mode is selected. X and Y are updated with a maximum accuracy of
eight digits.
minimum and maximum on the CALCULATE menu are calculated with a
tolerance of 1EL5; ‰f(x)dx is calculated at 1EL3. Therefore, the result
displayed may not be accurate to all eight displayed digits. For most
functions, at least five accurate digits exist. For fMin(, fMax(, and fnInt(
on the MATH menu and solve( in the CATALOG, the tolerance can be
specified.
TI-83 Plus
General Information
755
Function Limits
Function
Range of Input Values
0 |x| < 1012 (radian or degree)
L1 x 1
sin x, cos x, tan x
sinL1 x, cosL1
x
ln x, log x
10L100 < x < 10100
L10100 < x 230.25850929940
L10100 < x < 100
x
e
x
10
sinh x, cosh x
|x| 230.25850929940
|x| < 10100
tanh x
sinhL1
coshL1
tanhL1
x
|x| < 5 × 1099
x
1 x < 5 × 1099
x
L1 < x < 1
‡x (real mode)
‡x (complex mode)
x!
0 x < 10100
|x| < 10100
L.5 x 69, where x is a multiple of .5
TI-83 Plus
General Information
756
Texas Instruments (TI) Support and Service
For General Information
Home Page:
KnowledgeBase and
E-mail Inquiries:
Phone:
(800) TI-CARES; (800) 842-2737
For U.S., Canada, Mexico, Puerto
Rico, and Virgin Islands only
(Click the International Information
link.)
For Technical Support
KnowledgeBase and
Support by E-mail:
(972) 917-8324
Phone (not toll-free):
TI-83 Plus
General Information
758
For Product (hardware) Service
Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin
Islands: Always contact TI Customer Support before returning a
product for service.
All other customers: Refer to the leaflet enclosed with this product
(hardware) or contact your local TI retailer/distributor.
TI-83 Plus
General Information
759
Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments (“TI”) electronic product warranty extends only to the
original purchaser and user of the product.
Warranty Duration. This TI electronic product is warranted to the original
purchaser for a period of one (1) year from the original purchase date.
Warranty Coverage. This TI electronic product is warranted against defective
materials and construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS
BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER
SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR
CONSTRUCTION.
Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE,
INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN
DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT
BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR
CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE
CONSUMER OR ANY OTHER USER.
Some states/provinces do not allow the exclusion or limitation of implied
warranties or consequential damages, so the above limitations or exclusions
may not apply to you.
TI-83 Plus
General Information
760
Legal Remedies. This warranty gives you specific legal rights, and you may
also have other rights that vary from state to state or province to province.
Warranty Performance. During the above one (1) year warranty period, your
defective product will be either repaired or replaced with a reconditioned model
of an equivalent quality (at TI’s option) when the product is returned, postage
prepaid, to Texas Instruments Service Facility. The warranty of the repaired or
replacement unit will continue for the warranty of the original unit or six (6)
months, whichever is longer. Other than the postage requirement, no charge
will be made for such repair and/or replacement. TI strongly recommends that
you insure the product for value prior to mailing.
Software. Software is licensed, not sold. TI and its licensors do not warrant
that the software will be free from errors or meet your specific requirements.
All software is provided “AS IS.”
Copyright. The software and any documentation supplied with this product
are protected by copyright.
Australia & New Zealand Customers only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the original
purchaser and user of the product.
Warranty Duration. This Texas Instruments electronic product is warranted to
the original purchaser for a period of one (1) year from the original purchase
date.
TI-83 Plus
General Information
761
Warranty Coverage. This Texas Instruments electronic product is warranted
against defective materials and construction. This warranty is void if the
product has been damaged by accident or unreasonable use, neglect,
improper service, or other causes not arising out of defects in materials or
construction.
Warranty Disclaimers. Any implied warranties arising out of this sale,
including but not limited to the implied warranties of merchantability and
fitness for a particular purpose, are limited in duration to the above one-
year period. Texas Instruments shall not be liable for loss of use of the
product or other incidental or consequential costs, expenses, or
damages incurred by the consumer or any other user.
Except as expressly provided in the One-Year Limited Warranty for this
product, Texas Instruments does not promise that facilities for the repair
of this product or parts for the repair of this product will be available.
Some jurisdictions do not allow the exclusion or limitation of implied warranties
or consequential damages, so the above limitations or exclusions may not
apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may
also have other rights that vary from jurisdiction to jurisdiction.
Warranty Performance. During the above one (1) year warranty period, your
defective product will be either repaired or replaced with a new or
reconditioned model of an equivalent quality (at TI’s option) when the product
is returned to the original point of purchase. The repaired or replacement unit
will continue for the warranty of the original unit or six (6) months, whichever is
longer. Other than your cost to return the product, no charge will be made for
TI-83 Plus
General Information
762
such repair and/or replacement. TI strongly recommends that you insure the
product for value if you mail it.
Software. Software is licensed, not sold. TI and its licensors do not warrant
that the software will be free from errors or meet your specific requirements. All
software is provided “AS IS.”
Copyright. The software and any documentation supplied with this product
are protected by copyright.
All Other Customers
For information about the length and terms of the warranty, refer to your
package and/or to the warranty statement enclosed with this product, or
contact your local Texas Instruments retailer/distributor.
TI-83 Plus
General Information
763
Index
L1 (inverse), 64, 271, 694
æ (annual interest rate variable), 444,
å (exponent), 14, 20, 661
ì (graph style, animate), 117
í (graph style, dot), 117
ç (graph style, line), 117
ä (multiplication), 63, 695
Ú (number of payment periods
p (pi), 66
Ö (plot type, box), 371
Ò (plot type, histogram), 370
Õ (plot type, modified box), 370
Ô (plot type, normal probability), 372
TI-83 Plus
Index
764
2.PropZInt (two-proportion z
2.PropZTest (two-proportion z test),
2.SampTInt (two-sample t confidence
1.PropZInt (one-proportion z confidence
2.SampZInt (two-sample z confidence
2.Var Stats (two-variable statistics),
3 (cube), 68, 693
—A—
above graph style(é), 117
accuracy information
1.PropZTest (one-proportion z test),
1.Var Stats (one-variable statistics),
TI-83 Plus
Index
765
amortization
Asm(, 537, 655
AsmComp(, 537, 655
AsmPrgm(, 537, 655
augment(, 277, 307, 656
Automatic Power Down (APD), 6
axes, displaying (AxesOn, AxesOff),
ANGLE menu, 97
angle(, 90, 655
AxesOff, 127, 656
AxesOn, 127, 656
animate graph style (ì), 117
ANOVA( (one-way variance analysis),
—B—
APD (Automatic Power Down), 6
applications. See examples,
applications
Apps, 27, 598
AppVars, 27, 598
Archive, 30, 610, 655
below graph style (ê), 117
binomcdf(, 431, 656
binompdf(, 430, 656
box pixel mark (›), 235, 373
TI-83 Plus
Index
766
Boxplot plot type ( Ö), 371
—C—
ClrAllLists (clear all lists), 596, 657
ClrDraw (clear drawing), 217, 657
ClrHome (clear home screen), 532, 657
ClrList (clear list), 349, 658
ClrTable (clear table), 532, 658
C/Y (compounding-periods-per-year
CALCULATE menu, 147
Calculate output option, 388, 392
cash flow
CATALOG, 481
CBL/CBR
complex
CBL/CBR APP menu, 467
check memory, 596
compounding-periods-per-year variable
conj( (conjugate), 88, 658
Connected (plotting mode), 23, 658
Circle( (draw circle), 228, 657
Clear Entries, 596, 657
clearing
conversions
TI-83 Plus
Index
767
4DMS (to degrees/minutes/ seconds),
cube (3), 68, 693
CubicReg (cubic regression), 359, 658
cumSum( (cumulative sum), 279, 303,
4Nom (to nominal interest rate
4Rect (to rectangular conversion),
Equ4String( (equation-to-string
—D—
List4matr( (list-to-matrix
Matr4list( (matrix-to-list conversion),
P4Rx(, P4Ry( (polar-to-rectangular
R4Pr(, R4Pq( (rectangular-to-polar
String4Equ( (string-to-equation
data collection
CoordOff, 126, 658
CoordOn, 126, 658
cos( (cosine), 63, 658
TI-83 Plus
Index
768
Degree angle mode, 22, 97, 659
deleting items from memory, 599
DependAsk, 206, 209, 659
DependAuto, 206, 209, 659
derivative. See numerical derivative
DiagnosticOff, 354, 660
binomcdf(, 431, 656
binompdf(, 430, 656
geometcdf(, 433, 665
geometpdf(, 433, 665
invNorm(, 426, 668
normalcdf(, 426, 672
normalpdf(, 425, 673
poissoncdf(, 432, 675
poissonpdf(, 432, 675
tcdf(, 427, 687
DiagnosticOn, 354, 660
DIRECTNS, 471
DispGraph (display graph), 530, 660
tpdf(, 427, 687
distribution shading instructions
Shade_t(, 435, 684
ShadeNorm(, 435, 684
DMS (degrees/minutes/seconds entry
dot graph style (í), 117
DRAW menu, 214
DispTable (display table), 530, 661
DISTR DRAW (distributions drawing
DRAW POINTS menu, 233
distribution functions
TI-83 Plus
Index
769
DRAW STO (draw store menu), 239
drawing on a graph
ENTRY (last entry key), 33
Equ4String( (equation-to-string
Equation Solver, 72
lines (Horizontal, Line(, Vertical),
pixels (Pxl.Change, Pxl.Off, Pxl.On,
points (Pt.Change, Pt.Off, Pt.On),
errors
examples—applications
areas of regular n-sided polygons,
DrawInv (draw inverse), 224, 661
DuplicateName menu, 644
fundamental theorem of calculus,
—E—
Else, 514
TI-83 Plus
Index
770
examples—miscellaneous
calculating outstanding loan
parametric equations, ferris wheel
quadratic formula
expr( (string-to-expression conversion),
solving a system of nonlinear
examples—Getting Started
ExprOff (expression off), 128, 662
ExprOn (expression on), 128, 662
solving a system of linear equations,
—F—
Fill(, 276, 663
FINANCE CALC menu, 446
FINANCE VARS menu, 462
financial functions
TI-83 Plus
Index
771
function graphing
fnInt( (function integral), 71, 663
FnOff (function off), 115, 663
For(, 515, 664
defining on the home screen, in a
formulas
ANOVA, 722
overlaying functions on a graph,
TI-83 Plus
Index
772
Getting Started. See examples, Getting
Started
Y= editor, 111
Goto, 519, 665
ZOOM MEMORY menu, 144
ZOOM menu, 138
GraphStyle(, 524, 665
GridOff, 127, 666
—G—
GarbageCollect, 626, 664
GridOn, 127, 666
—H—
geometcdf(, 433, 665
geometpdf(, 433, 665
Get( (get data from CBL 2/CBL or
Histogram plot type (Ò), 370
Horiz (horizontal split-screen mode),
Horizontal (draw line), 221, 666
getKey, 531, 665
—I—
TI-83 Plus
Index
773
identity(, 277, 666
If instructions
inString( (in string), 492, 667
integral. See numerical integral
interest rate conversions
If-Then, 513, 666
If-Then-Else, 514, 667
IndpntAsk, 206, 209, 667
IndpntAuto, 206, 209, 667
inferential statistics. See stat tests;
confidence intervals
4Eff( (compute effective interest
4Nom( (compute nominal interest
intersect operation on a graph, 151
INTRVL (SEC), 475
calculating test results (Calculate),
inverse (L1), 64, 271, 694
inverse cumulative normal distribution
invNorm( (inverse cumulative normal
iPart( (integer part), 80, 273, 668
STAT TESTS menu, 394
test and interval output variables,
—K—
keyboard
Input, 526, 527, 667
TI-83 Plus
Index
774
LinReg(a+bx) (linear regression), 360,
LinReg(ax+b) (linear regression), 359,
LinRegTTest (linear regression t test),
LIST MATH menu, 311
LIST NAMES menu, 291
LIST OPS menu, 299
List4matr( (lists-to-matrix conversion),
—L—
LabelOff, 127, 668
LabelOn, 127, 668
labels
length( of string, 492, 669
line graph style (ç), 117
Line( (draw line), 220, 669
LINK RECEIVE menu, 644
LINK SEND menu, 634
linking
lists
using to graph a family of curves,
TI-83 Plus
Index
775
using to select data points from a
inverse (L1), 271
ln(, 65, 670
matrix math functions (det(, T, dim(,
Fill(, identity(, randM(, augment(,
Matr4list(, List4matr(, cumSum(),
log(, 65, 670
Logistic (regression), 361, 670
row operations(ref(, rref(, rowSwap(,
—M—
MATH CPX (complex menu), 88
MATH menu, 67
MATH NUM (number menu), 79
MATH PRB (probability menu), 92
Matr4list( (matrix-to-list conversion),
MATRX EDIT menu, 258
MATRX MATH menu, 274
MATRX NAMES menu, 265
max, 470
maximum operation on a graph, 150
mean(, 312, 671
median(, 312, 671
Mem Mgmt/Del menu, 597
memory
matrices
TI-83 Plus
Index
776
Normal (notation), 20, 672
Radian (angle), 22, 99, 678
Real, 24, 679
MEMORY menu, 596
Menu( (define menu), 521, 671
Sequential (graphing order), 24, 683
modified box plot type (Õ), 370
multiplication (ä), 63, 695
min, 470
minimum operation on a graph, 150
ModBoxplot plot type (Õ), 370
—N—
nDeriv( (numerical derivative), 70, 672
normal distribution probability
Normal notation mode, 20, 672
normal probability plot type (Ô), 372
normalcdf( (normal distribution
normalpdf( (probability density
Connected (plotting), 23, 658
Degree (angle), 22, 99, 659
Float (decimal), 21, 663
Full (screen), 25, 664
Func (graphing), 23, 664
Horiz (screen), 25, 666
NormProbPlot plot type (Ô), 372
TI-83 Plus
Index
777
Par/Param (parametric graphing mode),
parametric graphing
CALC (calculate operations on a
—O—
Omit, 619, 645
ON/HALT, 480
one-proportion z confidence interval
one-proportion z test (1.PropZTest),
one-sample t confidence interval
one-variable statistics (1.Var Stats),
Output(, 255, 530, 673
Overwrite, 619, 645
Y= editor, 158
path (ë) graph style, 117
Pause, 518, 674
Pen, 232
Overwrite All, 619
—P—
Pic (pictures), 239
P4Rx(, P4Ry( (polar-to-rectangular
P/Y (number-of-payment-periods-per-
TI-83 Plus
Index
778
PLOT, 476
Plot1(, 373, 674
Plot2(, 373, 674
Plot3(, 373, 674
Y= editor, 168
PlotsOff, 375, 675
PlotsOn, 375, 675
ZOOM operations, 174
PolarGC (polar graphing coordinates),
Pmt_Bgn (payment beginning variable),
Pmt_End (payment end variable), 461,
poissoncdf(, 432, 675
poissonpdf(, 432, 675
PRGM CTL (program control menu),
PRGM EDIT menu, 510
PRGM EXEC menu, 510
PRGM I/O (Input/Output menu), 525
PRGM NEW menu, 500
polar graphing
probability density function
CALC (calculate operations on a
prod( (product), 313, 676
programming
TI-83 Plus
Index
779
running assembly language
—R—
r (radian notation), 99, 692
R4Pr(, R4Pq( (rectangular-to-polar
r2, R2 (coefficients of determination),
Radian angle mode, 22, 99, 678
radian notation (r), 99, 692
RAM ARCHIVE ALL menu, 603
randBin( (random binomial), 96, 678
randInt( (random integer), 95, 679
randM( (random matrix), 277, 679
randNorm( (random Normal), 95, 679
Prompt, 528, 676
PwrReg (power regression), 361, 677
Real mode, 24, 679
real( (real part), 89, 679
RealTme, 476
—Q—
QuadReg (quadratic regression), 359,
RecallGDB, 244, 679
QuartReg (quartic regression), 360, 678
RecallPic, 241, 679
Quit, 619, 645
TI-83 Plus
Index
780
RectGC (rectangular graphing
RegEQ (regression equation variable),
—S—
Scatter plot type ("), 369
regression model
Select(, 304, 683
selecting
Repeat, 517, 680
RESET MEMORY menu, 608
resetting
functions from the home screen or a
Send( (send to CBL 2/CBL or CBR),
sending. See transmitting
seq( (sequence), 302, 683
sequence graphing
Return, 523, 680
round(, 80, 271, 680
row+(, 680
rowSwap(, 281, 680
TI-83 Plus
Index
781
shade below (ê) graph style, 117
Shade(, 226, 684
Shade_t(, 435, 684
ShadeNorm(, 435, 684
Simul (simultaneous graphing order
sin( (sine), 63, 685
Y= editor, 180
ZOOM (zoom menu), 191
Sequential (graphing order mode), 24,
setting
solve(, 77, 685
Solver, 72
solving for variables in the equation
split-screen modes from a program,
split-screen modes
SetUpEditor, 350, 683
shade above (é) graph style, 117
Horiz (horizontal) mode, 250
TI-83 Plus
Index
782
STAT CALC menu, 356
STAT EDIT menu, 348
1.PropZInt (one-proportion z
1.PropZTest (one-proportion z test),
2.PropZInt (two-proportion z
2.PropZTest (two-proportion z test),
2.SampÛTest (two-sample Û.Test),
2.SampTInt (two-sample t
2.SampTTest (two-sample t test),
stat list editor
attaching formulas to list names,
detaching formulas from list names,
editing elements of formula-
2.SampZInt (two-sample z
2.SampZTest (two-sample z test),
ANOVA( (one-way analysis of
LinRegTTest (linear regression t
restoring list names L1–L6, 333
STAT PLOTS menu, 373
stat tests and confidence intervals
TInterval (one-sample t confidence
ZInterval (one-sample z confidence
²
STAT TESTS menu, 394
TI-83 Plus
Index
783
statistical distribution functions. See
distribution functions
Boxplot (regular box plot), 371
Histogram, 370
ModBoxplot (modified box plot),
NormProbPlot (normal probability
Scatter, 369
student-t distribution
probability density function (tpdf(),
xyLine, 369
stdDev( (standard deviation), 314, 686
Stop, 523, 686
StoreGDB, 242, 686
StorePic, 239, 686
—T—
T (transpose matrix), 275, 693
TABLE SETUP screen, 205
tables
tan( (tangent), 63, 686
storing
String4Equ( (string-to-equation
strings
TI-83 Plus
Index
784
Tangent( (draw line), 222, 687
TblStart (table start variable), 205
tcdf( (student-t distribution probability),
TEST LOGIC (Boolean menu), 103
Text(
Then, 513, 666
thick (è) graph style, 117
TI.82
TI.83
Link. See linking
TI.83 Plus
æ variable (annual interest rate),
Ú variable (number of payment
C/Y variable (number of
compounding periods per year),
P/Y variable (number of payment
PMT variable (payment amount),
TVM Solver, 444
tvm_Ú (# payment periods), 450,
tvm_FV (future value), 451, 688
tvm_I% (interest rate), 449, 688
tvm_Pmt (payment amount), 449,
tvm_PV (present value), 450, 688
TInterval (one-sample t confidence
tpdf( (student-t distribution probability
TRACE
TI Connect, 632
time value of money (TVM)
TI-83 Plus
Index
785
tvm_I% (interest rate), 449, 688
tvm_Pmt (payment amount), 449, 688
tvm_PV (present value), 450, 688
two-proportion z confidence interval
transmitting
two-proportion z test (2.PropZTest),
two-variable statistics (2.Var Stats),
Type
transpose matrix (T), 275, 693
TRIGGER, 480
turning on and off
—U—
UnArchive, 30, 610, 689
calculator, 6
—V—
tvm_Ú (# payment periods), 450, 688
tvm_FV (future value), 451, 688
variables
TI-83 Plus
Index
786
—W—
While, 516, 689
window variables
variance( (variance of a list), 314, 689
VARS menu
—X—
XFact zoom factor, 145
xor (Boolean) exclusive or operator,
GDB, 44
Picture, 44
Statistics, 44
String, 44
th
x
xyLine (Ó) plot type, 369
Table, 44
Window, 44
Zoom, 44
Vertical (draw line), 221, 689
—Y—
Y.VARS menu
Function, 45
On/Off, 45
Parametric, 45
Polar, 45
TI-83 Plus
Index
787
Y= editor
YFact zoom factor, 145
Zoom In (zoom in), 140, 690
ZOOM MEMORY menu, 144
ZOOM menu, 138
Zoom Out (zoom out), 140, 690
ZoomFit (zoom to fit function), 143,
ZoomRcl (recall stored window), 145,
ZoomStat (statistics zoom), 143, 691
ZoomSto (store zoom window), 144,
ZPrevious (use previous window), 144,
—Z—
ZBox, 139, 690
ZDecimal, 141, 690
ZInteger, 143, 690
ZInterval (one-sample z confidence
ZSquare (set square pixels), 142, 691
ZStandard (use standard window), 142,
TI-83 Plus
Index
788
Quick-Find Locator
Documentation Conventions.....................................................................1
TI-83 Plus Keyboard.................................................................................2
Turning On and Turning Off the TI-83 Plus ..............................................6
Turning On the Calculator...................................................................6
Turning Off the Calculator...................................................................7
Batteries..............................................................................................7
Setting the Display Contrast .....................................................................8
When to Replace Batteries .................................................................9
The Display.............................................................................................10
Types of Displays..............................................................................10
Displaying Entries and Answers .......................................................10
Returning to the Home Screen .........................................................11
Busy Indicator ...................................................................................11
Display Cursors.................................................................................12
Entering Expressions and Instructions....................................................13
Entering an Expression.....................................................................13
Multiple Entries on a Line..................................................................14
TI-83 Plus
Quick-Find Locator
i
Entering a Number in Scientific Notation ..........................................14
Functions ..........................................................................................15
Instructions........................................................................................16
TI-83 Plus Edit Keys ...............................................................................17
Setting Modes.........................................................................................19
Changing Mode Settings...................................................................20
Setting a Mode from a Program........................................................20
Real, a+bi, re^qi ................................................................................24
Full, Horiz, G-T..................................................................................25
Using TI-83 Plus Variable Names...........................................................26
Variables and Defined Items.............................................................26
Notes about Variables.......................................................................27
Storing Variable Values ..........................................................................29
Storing Values in a Variable..............................................................29
Archiving Variables (Archive, Unarchive)..........................................30
Using Recall (RCL) ...........................................................................31
TI-83 Plus
Quick-Find Locator
ii
Accessing a Previous Entry ..............................................................34
Reexecuting the Previous Entry........................................................34
Multiple Entry Values on a Line ........................................................35
Clearing ENTRY ...............................................................................36
TI-83 Plus Menus....................................................................................39
Using a TI-83 Plus Menu ..................................................................39
Displaying a Menu ............................................................................40
Moving from One Menu to Another...................................................41
Scrolling a Menu ...............................................................................41
Leaving a Menu without Making a Selection.....................................43
VARS and VARS Y-VARS Menus ..........................................................44
VARS Menu ......................................................................................44
Selecting a Variable from the VARS Menu or VARS Y-VARS
Implied Multiplication.........................................................................48
Parentheses......................................................................................48
Negation............................................................................................49
Special Features of the TI-83 Plus .........................................................50
Flash – Electronic Upgradability .......................................................50
1.56 Megabytes (M) of Available Memory ........................................50
Applications.......................................................................................51
Archiving ...........................................................................................51
TI-83 Plus
Quick-Find Locator
iii
Calculator-Based Laboratory™ (CBL 2™, CBL™) and
Calculator-Based Ranger™ (CBR™)..........................................52
Other TI-83 Plus Features ......................................................................53
Graphing ...........................................................................................53
Tables ...............................................................................................54
Split Screen.......................................................................................54
Matrices ............................................................................................54
Lists...................................................................................................55
Statistics............................................................................................55
Inferential Statistics...........................................................................55
Applications.......................................................................................56
CATALOG.........................................................................................56
Programming ....................................................................................57
Archiving ...........................................................................................57
Communication Link .........................................................................57
Error Conditions......................................................................................59
Correcting an Error ...........................................................................60
Getting Started: Coin Flip .......................................................................61
Using Lists with Math Operations .....................................................63
Trigonometric Functions ...................................................................63
2
1
L
(Inverse)........................................................................................64
TI-83 Plus
Quick-Find Locator
iv
log(, 10^(, ln(.....................................................................................65
e^( (Exponential).................................................................................65
e (Constant) ......................................................................................65
L (Negation).......................................................................................66
p (Pi) .................................................................................................66
MATH Operations...................................................................................67
MATH Menu......................................................................................67
4Frac, 4Dec........................................................................................67
3
3
x
‡ (Root)...........................................................................................69
fMin(, fMax(.......................................................................................69
nDeriv( ..............................................................................................70
fnInt(..................................................................................................71
Using the Equation Solver ......................................................................72
Solver................................................................................................72
Entering an Expression in the Equation Solver.................................72
Entering and Editing Variable Values ...............................................74
Solving for a Variable in the Equation Solver....................................75
Editing an Equation Stored to eqn ....................................................77
Further Solutions...............................................................................77
Controlling the Solution for Solver or solve(......................................78
MATH NUM (Number) Operations..........................................................79
MATH NUM Menu.............................................................................79
abs(...................................................................................................79
round(................................................................................................80
iPart(, fPart(.......................................................................................80
TI-83 Plus
Quick-Find Locator
v
int( ....................................................................................................81
min(, max(.........................................................................................81
lcm(, gcd( ..........................................................................................82
Entering and Using Complex Numbers...................................................84
Entering Complex Numbers..............................................................85
Interpreting Complex Results............................................................86
Rectangular-Complex Mode .............................................................86
Polar-Complex Mode ........................................................................87
MATH CPX (Complex) Operations .........................................................88
MATH CPX Menu .............................................................................88
conj( ..................................................................................................88
real(...................................................................................................89
imag(.................................................................................................89
angle(................................................................................................90
abs(...................................................................................................90
4Rect .................................................................................................91
4Polar ................................................................................................91
MATH PRB (Probability) Operations.......................................................92
MATH PRB Menu .............................................................................92
rand...................................................................................................92
nPr, nCr.............................................................................................93
! (Factorial)........................................................................................94
randInt(..............................................................................................95
randNorm(.........................................................................................95
randBin( ............................................................................................96
TI-83 Plus
Quick-Find Locator
vi
ANGLE Menu....................................................................................97
Entry Notation ...................................................................................97
¡ (Degree) .........................................................................................98
r
(Radians) ........................................................................................99
8DMS................................................................................................99
TEST (Relational) Operations...............................................................101
=, ƒ, >, ‚, <, ..................................................................................101
TEST LOGIC (Boolean) Operations .....................................................103
and, or, xor......................................................................................103
Getting Started: Graphing a Circle........................................................105
Defining Graphs....................................................................................107
Displaying and Exploring a Graph ..................................................108
Saving a Graph for Later Use .........................................................108
Checking and Changing the Graphing Mode..................................109
Defining Functions................................................................................111
TI-83 Plus
Quick-Find Locator
vii
Displaying Functions in the Y= Editor .............................................111
Defining or Editing a Function.........................................................111
Defining a Function from the Home Screen or a Program..............112
Evaluating Y= Functions in Expressions.........................................113
Selecting and Deselecting Functions....................................................114
Selecting and Deselecting a Function.............................................114
Turning On or Turning Off a Stat Plot in the Y= Editor....................115
Selecting and Deselecting Functions from the Home Screen
Graph Style Icons in the Y= Editor..................................................117
Setting the Graph Style...................................................................118
Setting a Graph Style from a Program............................................120
Setting the Viewing Window Variables .................................................121
Displaying the Window Variables....................................................121
Changing a Window Variable Value ...............................................122
Storing to a Window Variable from the Home Screen or a
@X and @Y........................................................................................124
Setting the Graph Format .....................................................................125
TI-83 Plus
Quick-Find Locator
viii
Displaying Graphs ................................................................................129
Displaying a New Graph .................................................................129
Pausing or Stopping a Graph..........................................................129
Overlaying Functions on a Graph ...................................................130
Graphing a Family of Curves ..........................................................131
Exploring Graphs with the Free-Moving Cursor....................................132
Exploring Graphs with TRACE..............................................................134
Moving the Trace Cursor ................................................................134
Moving the Trace Cursor from Function to Function.......................135
Moving the Trace Cursor to Any Valid X Value...............................135
Panning to the Left or Right ............................................................136
Leaving and Returning to TRACE...................................................137
ZBox................................................................................................139
ZDecimal.........................................................................................141
ZSquare ..........................................................................................142
ZStandard .......................................................................................142
TI-83 Plus
Quick-Find Locator
ix
ZTrig................................................................................................142
ZInteger...........................................................................................143
ZoomStat ........................................................................................143
ZoomFit...........................................................................................143
ZPrevious........................................................................................144
ZoomSto .........................................................................................144
ZoomRcl..........................................................................................145
Checking XFact and YFact .............................................................145
Changing XFact and YFact.............................................................146
Using ZOOM MEMORY Menu Items from the Home Screen
Using the CALC (Calculate) Operations ...............................................147
value ...............................................................................................147
zero.................................................................................................148
intersect ..........................................................................................151
dy/dx ...............................................................................................152
‰f(x)dx ..............................................................................................153
Getting Started: Path of a Ball ..............................................................154
TI-83 Plus Graphing Mode Similarities ...........................................158
Setting Parametric Graphing Mode.................................................158
TI-83 Plus
Quick-Find Locator
x
Displaying the Parametric Y= Editor ...............................................158
Selecting a Graph Style ..................................................................159
Defining and Editing Parametric Equations ....................................159
Setting the Graph Format ...............................................................161
Displaying a Graph .........................................................................161
Exploring Parametric Graphs................................................................163
TRACE............................................................................................163
ZOOM .............................................................................................165
CALC ..............................................................................................165
TI-83 Plus Graphing Mode Similarities ...........................................168
Setting Polar Graphing Mode..........................................................168
Displaying the Polar Y= Editor ........................................................168
Selecting Graph Styles ...................................................................169
Defining and Editing Polar Equations .............................................169
Setting the Graph Format ...............................................................171
Displaying a Graph .........................................................................171
TI-83 Plus
Quick-Find Locator
xi
Exploring Polar Graphs.........................................................................173
TRACE............................................................................................173
ZOOM .............................................................................................174
CALC ..............................................................................................175
Getting Started: Forest and Trees ........................................................176
Defining and Displaying Sequence Graphs ..........................................179
TI-83 Plus Graphing Mode Similarities ...........................................179
Setting Sequence Graphing Mode..................................................179
TI-83 Plus Sequence Functions u, v, and w ...................................179
Displaying the Sequence Y= Editor ................................................180
Selecting Graph Styles ...................................................................181
Selecting and Deselecting Sequence Functions.............................181
Nonrecursive Sequences................................................................182
Selecting Axes Combinations ...............................................................187
Setting the Graph Format ...............................................................187
Setting Axes Format .......................................................................187
Displaying a Sequence Graph ........................................................188
TRACE............................................................................................189
TI-83 Plus
Quick-Find Locator
xii
ZOOM .............................................................................................191
CALC ..............................................................................................191
Evaluating u, v, and w.....................................................................192
Graphing a Web Plot.......................................................................193
Using Web Plots to Illustrate Convergence ..........................................195
Example: Convergence...................................................................195
Example: Predator-Prey Model.......................................................197
Comparing TI-83 Plus and TI-82 Sequence Variables .........................201
Sequences and Window Variables .................................................201
Sequence Keystroke Changes .......................................................202
Getting Started: Roots of a Function ....................................................203
Setting Up the Table.............................................................................205
TABLE SETUP Screen ...................................................................205
TblStart, @Tbl...................................................................................205
Defining Dependent Variables from the Y= Editor ..........................207
TI-83 Plus
Quick-Find Locator
xiii
Displaying the Table .............................................................................209
The Table........................................................................................209
Independent and Dependent Variables ..........................................209
Clearing the Table from the Home Screen or a Program ...............210
Getting Started: Drawing a Tangent Line .............................................212
Using the DRAW Menu.........................................................................214
Before Drawing on a Graph ............................................................215
Clearing Drawings ................................................................................217
Clearing Drawings When a Graph Is Displayed..............................217
Clearing Drawings from the Home Screen or a Program ...............217
Drawing Line Segments........................................................................218
Drawing a Line Segment Directly on a Graph.................................218
Drawing a Line Segment from the Home Screen or a Program .....219
Drawing a Line from the Home Screen or a Program.....................221
Drawing a Tangent Line Directly on a Graph..................................222
Drawing a Tangent Line from the Home Screen or a Program.......223
Drawing Functions and Inverses ..........................................................224
Drawing an Inverse of a Function ...................................................224
TI-83 Plus
Quick-Find Locator
xiv
Shading Areas on a Graph ...................................................................226
Drawing Circles.....................................................................................228
Drawing a Circle Directly on a Graph..............................................228
Drawing a Circle from the Home Screen or a Program ..................229
Placing Text Directly on a Graph ....................................................230
Split Screen.....................................................................................231
Drawing Points on a Graph...................................................................233
Drawing Points from the Home Screen or a Program.....................235
Drawing Pixels......................................................................................237
Split Screen.....................................................................................238
Storing a Graph Picture ..................................................................239
Recalling Graph Pictures (Pic)..............................................................241
Deleting a Graph Picture.................................................................241
TI-83 Plus
Quick-Find Locator
xv
What Is a Graph Database? ...........................................................242
Storing a Graph Database ..............................................................242
Recalling Graph Databases (GDB).......................................................244
Recalling a Graph Database...........................................................244
Deleting a Graph Database ............................................................245
Getting Started: Exploring the Unit Circle .............................................246
Using Split Screen ................................................................................248
Setting a Split-Screen Mode ...........................................................248
Moving from Half to Half in Horiz Mode ..........................................251
Full Screens in Horiz Mode.............................................................251
DRAW POINTS Menu Pixel Instructions ........................................254
DRAW Menu Text( Instruction ........................................................254
PRGM I/O Menu Output( Instruction...............................................255
Setting a Split-Screen Mode from the Home Screen or a
TI-83 Plus
Quick-Find Locator
xvi
Defining a Matrix...................................................................................258
Viewing and Editing Matrix Elements....................................................260
Displaying Matrix Elements.............................................................260
Editing-Context Keys ......................................................................264
Using Matrices with Expressions ..........................................................265
Using a Matrix in an Expression .....................................................265
Entering a Matrix in an Expression .................................................265
Copying One Matrix to Another.......................................................267
Accessing a Matrix Element............................................................268
Using Math Functions with Matrices ...............................................269
L (Negation).....................................................................................270
abs(.................................................................................................271
round(..............................................................................................271
M1
TI-83 Plus
Quick-Find Locator
xvii
Powers............................................................................................272
Relational Operations .....................................................................272
iPart(, fPart(, int(..............................................................................273
Using the MATRX MATH Operations ...................................................274
T
Accessing Matrix Dimensions with dim(..........................................275
Creating a Matrix with dim( .............................................................276
Redimensioning a Matrix with dim( ...................................................276
identity( ...........................................................................................277
randM(.............................................................................................277
augment(.........................................................................................277
Matr4list(..........................................................................................278
List4matr(.........................................................................................279
ref(, rref(..........................................................................................280
row+(...............................................................................................281
ärow(...............................................................................................282
ärow+(.............................................................................................282
Getting Started: Generating a Sequence..............................................283
Naming Lists.........................................................................................286
Using TI-83 Plus List Names L1 through L6 ...................................286
TI-83 Plus
Quick-Find Locator
xviii
Creating a List Name on the Home Screen ....................................286
Copying One List to Another...........................................................289
Using Lists in Graphing...................................................................290
Entering List Names .............................................................................291
Using the LIST NAMES Menu ........................................................291
Attaching a Formula to a List Name................................................293
Attaching a Formula to a List on the Home Screen or in a
Detaching a Formula from a List.....................................................296
Using a List in an Expression..........................................................297
Using Lists with Math Functions .....................................................298
LIST OPS Menu....................................................................................299
Using dim( to Find List Dimensions ................................................301
Using dim( to Create a List .............................................................301
Using dim( to Redimension a List ...................................................301
seq(.................................................................................................302
TI-83 Plus
Quick-Find Locator
xix
@List(...............................................................................................303
Select(.............................................................................................304
Using Select( to Select Data Points from a Plot..............................305
augment(.........................................................................................307
List4matr(.........................................................................................308
Matr4list(..........................................................................................308
min(, max(.......................................................................................311
sum(, prod(......................................................................................313
Sums and Products of Numeric Sequences ...................................313
Setting Up Statistical Analyses .............................................................328
Using Lists to Store Data ................................................................328
Setting Up a Statistical Analysis .....................................................328
Using the Stat List Editor ......................................................................330
Entering a List Name in the Stat List Editor ....................................330
Creating a Name in the Stat List Editor...........................................332
Removing a List from the Stat List Editor........................................332
Editing a List Element .....................................................................334
TI-83 Plus
Quick-Find Locator
xx
Attaching a Formula to a List Name in Stat List Editor ...................336
Using the Stat List Editor When Formula-Generated Lists Are
Handling Errors Resulting from Attached Formulas........................339
Detaching Formulas from List Names ..................................................340
Detaching a Formula from a List Name ..........................................340
Editing an Element of a Formula-Generated List............................341
Stat List Editor Contexts .................................................................342
Stat List Editor Contexts .......................................................................344
View-Elements Context...................................................................344
Edit-Elements Context ....................................................................344
View-Names Context ......................................................................346
Enter-Name Context .......................................................................346
ClrList..............................................................................................349
Regression Model Features..................................................................352
Regression Model Features............................................................352
Automatic Residual List ..................................................................352
Automatic Regression Equation......................................................353
Diagnostics Display Mode...............................................................354
TI-83 Plus
Quick-Find Locator
xxi
Frequency of Occurrence for Data Points.......................................357
1.Var Stats......................................................................................357
2.Var Stats......................................................................................358
2
3
4
2
3
2
x
b
Lbx
SinReg Example: Daylight Hours in Alaska for One Year ...............363
Statistical Analysis in a Program...........................................................367
Steps for Plotting Statistical Data in Lists .......................................368
" (Scatter) .....................................................................................369
TI-83 Plus
Quick-Find Locator
xxii
Displaying Other Stat Plot Editors...................................................375
Turning On and Turning Off Stat Plots............................................375
Defining the Viewing Window .........................................................376
Tracing a Stat Plot ..........................................................................376
Defining a Stat Plot in a Program....................................................378
Getting Started: Mean Height of a Population ......................................381
Height (in centimeters) of Each of 10 Women ................................381
Inferential Stat Editors ..........................................................................388
Using an Inferential Stat Editor .......................................................388
Selecting Data or Stats ...................................................................390
Selecting the Pooled Option ...........................................................391
Selecting Calculate or Draw for a Hypothesis Test.........................392
Inferential Stat Editors for the STAT TESTS Instructions ...............395
Z.Test .............................................................................................396
T.Test .............................................................................................397
TI-83 Plus
Quick-Find Locator
xxiii
ZInterval..........................................................................................405
TInterval..........................................................................................406
1.PropZInt.......................................................................................410
2.PropZInt.......................................................................................411
2
c .Test............................................................................................412
ANOVA( ..........................................................................................417
Test and Interval Output Variables .......................................................422
Distribution Functions ...........................................................................424
normalpdf(.......................................................................................425
normalcdf(.......................................................................................426
invNorm( .........................................................................................426
tpdf(.................................................................................................427
tcdf(.................................................................................................427
2
c pdf(..............................................................................................428
2
c cdf(..............................................................................................429
Üpdf( ...............................................................................................429
binompdf .........................................................................................430
binomcdf( ........................................................................................431
TI-83 Plus
Quick-Find Locator
xxiv
poissonpdf( .....................................................................................432
poissoncdf(......................................................................................432
Distribution Shading..............................................................................434
Shade_t( .........................................................................................435
2
Shadec ( ........................................................................................436
ShadeÜ(..........................................................................................437
Chapter 14: Applications .............................................................. 438
The Applications Menu .........................................................................438
Getting Started: Financing a Car ..........................................................440
Getting Started: Computing Compound Interest...................................442
Using the Financial Functions...............................................................446
Entering Cash Inflows and Cash Outflows......................................446
Calculating Time Value of Money ...................................................448
tvm_Pmt..........................................................................................449
tvm_æ.............................................................................................449
tvm_PV ...........................................................................................450
tvm_Ú..............................................................................................450
TI-83 Plus
Quick-Find Locator
xxv
tvm_FV............................................................................................451
Calculating Cash Flows ........................................................................452
Calculating a Cash Flow .................................................................452
npv(, irr(...........................................................................................453
Calculating an Amortization Schedule ............................................454
GPrn(, GInt(......................................................................................455
Amortization Example: Calculating an Outstanding Loan
4Nom(..............................................................................................459
4Eff(.................................................................................................459
Finding Days between Dates/Defining Payment Method ..........................460
dbd(.................................................................................................460
Defining the Payment Method.........................................................461
Pmt_End .........................................................................................461
Pmt_Bgn .........................................................................................461
FINANCE VARS Menu ...................................................................462
The CBL/CBR Application.....................................................................464
Data Collection Methods and Options ..................................................467
TI-83 Plus
Quick-Find Locator
xxvi
Specifying the Data Collection Method from the CBL/CBR
Specifying Options for Each Data Collection Method .....................468
TYPE...............................................................................................469
UNITS .............................................................................................470
DIRECTNS (Directions) ..................................................................471
Data Collection Comments and Results .........................................471
UNITS .............................................................................................475
PLOT...............................................................................................476
DIRECTNS (Directions) ..................................................................476
Data Collection Results...................................................................477
Stopping Data Collection ......................................................................480
Browsing the TI-83 Plus CATALOG......................................................481
What Is the CATALOG?..................................................................481
TI-83 Plus
Quick-Find Locator
xxvii
Storing a String to a String Variable................................................487
Displaying the Contents of a String Variable ..................................488
String Functions and Instructions in the CATALOG..............................489
Selecting a String Function from the CATALOG.............................490
Equ4String(......................................................................................491
expr(................................................................................................491
inString(...........................................................................................492
length(.............................................................................................492
String4Equ(......................................................................................493
sub(.................................................................................................493
Entering a Function to Graph during Program Execution ...............494
Hyperbolic Functions in the CATALOG ................................................495
Hyperbolic Functions ......................................................................495
sinh(, cosh(, tanh( ...........................................................................496
1
1
1
Chapter 16: Programming............................................................. 497
Getting Started: Volume of a Cylinder ..................................................497
Creating and Deleting Programs ..........................................................500
Creating a New Program ................................................................500
Managing Memory and Deleting a Program ...................................501
TI-83 Plus
Quick-Find Locator
xxviii
Entering a Program Command Line ...............................................504
Executing a Program ......................................................................505
Editing Programs ..................................................................................507
Inserting and Deleting Command Lines..........................................508
Copying and Renaming Programs........................................................509
Copying and Renaming a Program.................................................509
Controlling Program Flow ...............................................................512
If.Then ............................................................................................513
For( .................................................................................................515
While...............................................................................................516
Repeat ............................................................................................517
Pause..............................................................................................518
Lbl, Goto .........................................................................................519
IS>( .................................................................................................520
DS<(................................................................................................521
Menu(..............................................................................................521
prgm................................................................................................522
Return .............................................................................................523
Stop.................................................................................................523
DelVar.............................................................................................523
TI-83 Plus
Quick-Find Locator
xxix
PRGM I/O (Input/Output) Instructions...................................................525
Prompt ............................................................................................528
Displaying the Home Screen ..........................................................528
DispTable........................................................................................530
Output(............................................................................................530
getKey.............................................................................................531
TI-83 Plus Key Code Diagram ........................................................532
GetCalc(..........................................................................................533
Get(, Send( .....................................................................................533
Calling Other Programs as Subroutines ...............................................535
Calling a Program from Another Program.......................................535
Entering a Calculation.....................................................................540
Converting to a Fraction..................................................................542
Displaying Complex Results ...........................................................544
Box with Lid ..........................................................................................546
TI-83 Plus
Quick-Find Locator
xxx
Defining a Table of Values..............................................................547
Setting the Viewing Window ...........................................................551
Displaying and Tracing the Graph ..................................................553
Finding the Calculated Maximum....................................................557
Problem...........................................................................................560
Procedure .......................................................................................561
Graphing Piecewise Functions .............................................................564
Problem...........................................................................................564
Procedure .......................................................................................564
Graphing Inequalities............................................................................566
Problem...........................................................................................566
Procedure .......................................................................................566
Solving a System of Nonlinear Equations.............................................568
Problem...........................................................................................568
Procedure .......................................................................................568
Program ..........................................................................................570
Graphing Cobweb Attractors ................................................................572
Problem...........................................................................................572
Procedure .......................................................................................572
Using a Program to Guess the Coefficients..........................................574
Setting Up the Program ..................................................................574
Program ..........................................................................................574
TI-83 Plus
Quick-Find Locator
xxxi
Problem...........................................................................................576
Procedure .......................................................................................576
Finding the Area between Curves ........................................................578
Problem...........................................................................................578
Procedure .......................................................................................578
Using Parametric Equations: Ferris Wheel Problem.............................580
Problem...........................................................................................580
Procedure .......................................................................................581
Demonstrating the Fundamental Theorem of Calculus ........................584
Problem 1........................................................................................584
Problem 2........................................................................................586
Computing Areas of Regular N-Sided Polygons...................................588
Problem...........................................................................................588
Procedure .......................................................................................588
Computing and Graphing Mortgage Payments ....................................592
Problem...........................................................................................592
Procedure .......................................................................................592
Checking Available Memory .................................................................596
Displaying the MEMORY MANAGEMENT/DELETE Menu.............597
Deleting Items from Memory.................................................................599
Clearing Entries and List Elements.......................................................601
Clear Entries ...................................................................................601
TI-83 Plus
Quick-Find Locator
xxxii
ClrAllLists........................................................................................602
Resetting the TI-83 Plus .......................................................................603
RAM ARCHIVE ALL Menu..............................................................603
Resetting RAM Memory..................................................................604
Resetting Archive Memory..............................................................606
Resetting All Memory......................................................................608
Archiving and UnArchiving Variables....................................................610
Grouping and Ungrouping Variables ....................................................616
Grouping Variables .........................................................................616
Ungrouping Variables .....................................................................619
DuplicateName Menu .....................................................................619
Garbage Collection...............................................................................622
Garbage Collection Message..........................................................622
Responding to the Garbage Collection Message ...........................622
Why Not Perform Garbage Collection Automatically Without a
Why Is Garbage Collection Necessary? .........................................623
How Unarchiving a Variable Affects the Process............................625
If the MEMORY Screen Shows Enough Free Space......................626
Using the GarbageCollect Command .............................................627
TI-83 Plus
Quick-Find Locator
xxxiii
Chapter 19: Communication Link ................................................ 629
Linking to a Computer.....................................................................633
Stopping a Transmission ................................................................637
Receiving Items ....................................................................................644
LINK RECEIVE Menu .....................................................................644
DuplicateName Menu .....................................................................644
Receiving from a TI-83....................................................................646
Receiving from a TI-82 — Unresolved Differences.........................647
Receiving from a TI-73....................................................................648
Memory Backup Complete..............................................................651
Error Conditions....................................................................................652
TI-83 Plus
Quick-Find Locator
xxxiv
TI-83 Plus Menu Map ...........................................................................698
Variables...............................................................................................718
Statistics Formulas ...............................................................................721
Logistic............................................................................................721
SinReg ............................................................................................722
ANOVA( ..........................................................................................722
Financial Formulas ...............................................................................728
Interest Rate Conversions ..............................................................733
Battery Information ...............................................................................735
When to Replace the Batteries .......................................................735
Battery Precautions.........................................................................737
Replacing the Batteries...................................................................737
TI-83 Plus
Quick-Find Locator
xxxv
In Case of Difficulty...............................................................................739
Handling a Difficulty ........................................................................739
Error Conditions....................................................................................742
Support and Service Information ..........................................................758
Warranty Information ............................................................................760
Australia & New Zealand Customers only ......................................761
All Customers Outside the U.S. and Canada..................................763
TI-83 Plus
Quick-Find Locator
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