TI-83
GRAPHING CALCULATOR
GUIDEBOOK
TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR,
Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas
Instruments Incorporated.
IBM is a registered trademark of International Business Machines Corporation.
Macintosh is a registered trademark of Apple Computer, Inc.
Windows is a registered trademark of Microsoft Corporation.
© 1996, 2000, 2001 Texas Instruments Incorporated.
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Table of Contents
This manual describes how to use the TI.83 Graphing Calculator. Getting
Started is an overview of TI.83 features. Chapter 1 describes how the TI.83
operates. Other chapters describe various interactive features. Chapter 17
shows how to combine these features to solve problems.
Getting Started:
Do This First!
TI-83 Keyboard ..........................................
TI-83 Menus .............................................
First Steps ...............................................
Entering a Calculation: The Quadratic Formula ..........
Converting to a Fraction: The Quadratic Formula........
Displaying Complex Results: The Quadratic Formula ....
Defining a Function: Box with Lid .......................
Defining a Table of Values: Box with Lid.................
Zooming In on the Table: Box with Lid...................
Setting the Viewing Window: Box with Lid...............
Displaying and Tracing the Graph: Box with Lid .........
Zooming In on the Graph: Box with Lid ..................
Finding the Calculated Maximum: Box with Lid..........
Other TI-83 Features.....................................
2
4
5
6
7
8
9
10
11
12
13
15
16
17
Chapter 1:
Operating the
TI-83
Turning On and Turning Off the TI-83.................... 1-2
Setting the Display Contrast ............................. 1-3
The Display.............................................. 1-4
Entering Expressions and Instructions................... 1-6
TI-83 Edit Keys .......................................... 1-8
Setting Modes ........................................... 1-9
Using TI-83 Variable Names ............................. 1-13
Storing Variable Values .................................. 1-14
Recalling Variable Values ................................ 1-15
ENTRY (Last Entry) Storage Area........................ 1-16
Ans (Last Answer) Storage Area ......................... 1-18
TI-83 Menus ............................................. 1-19
VARS and VARS Y.VARS Menus......................... 1-21
Equation Operating System (EOSé) ..................... 1-22
Error Conditions......................................... 1-24
Introduction iii
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Chapter 2:
Getting Started: Coin Flip................................ 2-2
Math, Angle, and Keyboard Math Operations .............................. 2-3
Test Operations
MATH Operations........................................ 2-5
MATH NUM (Number) Operations........................ 2-13
Entering and Using Complex Numbers................... 2-16
MATH CPX (Complex) Operations ....................... 2-18
MATH PRB (Probability) Operations ..................... 2-20
ANGLE Operations....................................... 2-23
TEST (Relational) Operations............................ 2-25
TEST LOGIC (Boolean) Operations ...................... 2-26
Chapter 3:
Function
Graphing
Getting Started: Graphing a Circle ....................... 3-2
Defining Graphs ......................................... 3-3
Setting the Graph Modes................................. 3-4
Defining Functions ...................................... 3-5
Selecting and Deselecting Functions..................... 3-7
Setting Graph Styles for Functions....................... 3-9
Setting the Graph Format ................................ 3-13
Displaying Graphs ....................................... 3-15
Exploring Graphs with the Free-Moving Cursor.......... 3-17
Exploring Graphs with TRACE........................... 3-18
Using ZOOM MEMORY .................................. 3-23
Using the CALC (Calculate) Operations .................. 3-25
Chapter 4:
Parametric
Graphing
Getting Started: Path of a Ball ........................... 4-2
Defining and Displaying Parametric Graphs.............. 4-4
Exploring Parametric Graphs ............................ 4-7
Chapter 5:
Polar Graphing
Getting Started: Polar Rose .............................. 5-2
Defining and Displaying Polar Graphs ................... 5-3
Exploring Polar Graphs.................................. 5-6
iv Introduction
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Chapter 6:
Sequence
Graphing
Getting Started: Forest and Trees ........................ 6-2
Selecting Axes Combinations ............................ 6-8
Exploring Sequence Graphs.............................. 6-9
Graphing Web Plots...................................... 6-11
Using Web Plots to Illustrate Convergence............... 6-12
Graphing Phase Plots .................................... 6-13
Keystroke Differences Between TI-83 and TI-82 ......... 6-16
Chapter 7:
Tables
Getting Started: Roots of a Function ..................... 7-2
Setting Up the Table ..................................... 7-3
Defining the Dependent Variables........................ 7-4
Displaying the Table ..................................... 7-5
Chapter 8:
DRAW
Operations
Getting Started: Drawing a Tangent Line................. 8-2
Using the DRAW Menu................................... 8-3
Clearing Drawings ....................................... 8-4
Drawing Line Segments.................................. 8-5
Drawing Horizontal and Vertical Lines ................... 8-6
Drawing Tangent Lines .................................. 8-8
Drawing Functions and Inverses......................... 8-9
Shading Areas on a Graph ............................... 8-10
Drawing Circles.......................................... 8-11
Using Pen to Draw on a Graph ........................... 8-13
Drawing Points on a Graph .............................. 8-14
Drawing Pixels .......................................... 8-16
Storing Graph Pictures (Pic) ............................. 8-17
Recalling Graph Pictures (Pic) ........................... 8-18
Storing Graph Databases (GDB) ......................... 8-19
Recalling Graph Databases (GDB) ....................... 8-20
Chapter 9:
Split Screen
Getting Started: Exploring the Unit Circle................ 9-2
Using Split Screen ....................................... 9-3
Horiz (Horizontal) Split Screen........................... 9-4
G-T (Graph-Table) Split Screen .......................... 9-5
TI.83 Pixels in Horiz and G-T Modes ..................... 9-6
Introduction v
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Chapter 10:
Matrices
Getting Started: Systems of Linear Equations ............ 10-2
Defining a Matrix ........................................ 10-3
Viewing and Editing Matrix Elements.................... 10-4
Using Matrices with Expressions ........................ 10-7
Displaying and Copying Matrices ........................ 10-8
Using Math Functions with Matrices..................... 10-9
Using the MATRX MATH Operations ..................... 10-12
Chapter 11:
Lists
Naming Lists............................................. 11-3
Storing and Displaying Lists ............................. 11-4
Entering List Names ..................................... 11-6
Attaching Formulas to List Names ....................... 11-7
Using Lists in Expressions ............................... 11-9
LIST OPS Menu.......................................... 11-10
LIST MATH Menu ........................................ 11-17
Chapter 12:
Statistics
Getting Started: Pendulum Lengths and Periods ......... 12-2
Setting up Statistical Analyses ........................... 12-10
Using the Stat List Editor ................................ 12-11
Attaching Formulas to List Names ....................... 12-14
Detaching Formulas from List Names.................... 12-16
Switching Stat List Editor Contexts ...................... 12-17
Stat List Editor Contexts................................. 12-18
Regression Model Features .............................. 12-22
STAT CALC Menu........................................ 12-24
Statistical Variables...................................... 12-29
Statistical Analysis in a Program ......................... 12-30
Statistical Plotting ....................................... 12-31
Statistical Plotting in a Program ......................... 12-37
Chapter 13:
Inferential
Statistics and
Distributions
Getting Started: Mean Height of a Population ............ 13-2
Inferential Stat Editors................................... 13-6
STAT TESTS Menu ...................................... 13-9
Inferential Statistics Input Descriptions.................. 13-26
Test and Interval Output Variables....................... 13-28
Distribution Functions................................... 13-29
Distribution Shading..................................... 13-35
vi Introduction
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Chapter 14:
Financial
Functions
Getting Started: Financing a Car ......................... 14-2
Getting Started: Computing Compound Interest.......... 14-3
Using the TVM Solver .................................... 14-4
Calculating Time Value of Money (TVM) ................. 14-6
Calculating Cash Flows .................................. 14-8
Calculating Amortization ................................ 14-9
Calculating Interest Conversion.......................... 14-12
Finding Days between Dates/Defining Payment Method ..... 14-13
Chapter 15:
CATALOG,
Strings,
Hyperbolic
Functions
Browsing the TI-83 CATALOG ........................... 15-2
Entering and Using Strings............................... 15-3
Storing Strings to String Variables ....................... 15-4
String Functions and Instructions in the CATALOG ...... 15-6
Hyperbolic Functions in the CATALOG .................. 15-10
Chapter 16:
Programming
Creating and Deleting Programs ......................... 16-4
Entering Command Lines and Executing Programs ...... 16-5
Editing Programs ........................................ 16-6
Copying and Renaming Programs........................ 16-7
PRGM CTL (Control) Instructions ....................... 16-8
PRGM I/O (Input/Output) Instructions ................... 16-16
Calling Other Programs as Subroutines .................. 16-22
Chapter 17:
Applications
Comparing Test Results Using Box Plots ................ 17-2
Graphing Piecewise Functions........................... 17-4
Graphing Inequalities .................................... 17-5
Solving a System of Nonlinear Equations ................ 17-6
Using a Program to Create the Sierpinski Triangle ....... 17-7
Graphing Cobweb Attractors ............................ 17-8
Using a Program to Guess the Coefficients............... 17-9
Graphing the Unit Circle and Trigonometric Curves...... 17-10
Finding the Area between Curves ........................ 17-11
Using Parametric Equations: Ferris Wheel Problem...... 17-12
Demonstrating the Fundamental Theorem of Calculus... 17-14
Computing Areas of Regular N-Sided Polygons .......... 17-16
Computing and Graphing Mortgage Payments ........... 17-18
Introduction vii
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Chapter 18:
Memory
Management
Checking Available Memory ............................. 18-2
Deleting Items from Memory ............................ 18-3
Clearing Entries and List Elements ...................... 18-4
Resetting the TI.83 ...................................... 18-5
Chapter 19:
Communication
Link
Getting Started: Sending Variables ....................... 19-2
Selecting Items to Send .................................. 19-4
Receiving Items.......................................... 19-5
Transmitting Items....................................... 19-6
Transmitting Lists to a TI-82 ............................. 19-8
Transmitting from a TI-82 to a TI-83 ..................... 19-9
Appendix A:
Tables and
Reference
Table of Functions and Instructions ..................... A-2
Menu Map ............................................... A-39
Variables ................................................ A-49
Statistical Formulas ..................................... A-50
Financial Formulas ...................................... A-54
Information
Appendix B:
General
Information
Battery Information...................................... B-2
In Case of Difficulty ..................................... B-4
Error Conditions......................................... B-5
Accuracy Information.................................... B-10
Support and Service Information......................... B-12
Warranty Information.................................... B-13
Index
viii Introduction
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Getting Started:
Do This First!
Contents
TI-83 Keyboard ..........................................
TI-83 Menus .............................................
First Steps ...............................................
Entering a Calculation: The Quadratic Formula ..........
Converting to a Fraction: The Quadratic Formula........
Displaying Complex Results: The Quadratic Formula ....
Defining a Function: Box with Lid .......................
Defining a Table of Values: Box with Lid.................
Zooming In on the Table: Box with Lid...................
Setting the Viewing Window: Box with Lid...............
Displaying and Tracing the Graph: Box with Lid .........
Zooming In on the Graph: Box with Lid ..................
Finding the Calculated Maximum: Box with Lid..........
Other TI.83 Features.....................................
2
4
5
6
7
8
9
10
11
12
13
15
16
17
Getting Started 1
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TI-83 Keyboard
Generally, the keyboard is divided into these zones: graphing keys, editing
keys, advanced function keys, and scientific calculator keys.
Keyboard Zones Graphing keys access the interactive graphing features.
Editing keys allow you to edit expressions and values.
Advanced function keys display menus that access the
advanced functions.
Scientific calculator keys access the capabilities of a
standard scientific calculator.
Graphing Keys
Editing Keys
Advanced
Function Keys
Scientific
Calculator Keys
2 Getting Started
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Using the
Color-Coded
Keyboard
The keys on the TI.83 are color-coded to help you easily
locate the key you need.
The 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 primary function of each key is printed in white on the
key. 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 [TEST].
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.
Getting Started 3
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TI-83 Menus
Displaying a Menu
While using your TI.83, 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.
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.
Selecting an Item from a Menu
The number or letter next to the current menu
item is highlighted. If the menu continues
beyond the screen, a down arrow ( $ )
replaces the colon ( : ) in the last displayed
item. If you scroll beyond the last displayed
item, an up arrow ( # ) replaces the colon in
the first item displayed.You can select an item
in either of two ways.
¦ Press † or } to move the cursor to the
number or letter of the item; press Í.
¦ Press the key or key combination for the
number or letter next to the item.
Leaving a Menu without Making a Selection
You can leave a menu without making a
selection in any of three ways.
¦ Press ‘ to return to the screen
where you were.
¦ Press y [QUIT] to return to the home
screen.
¦ Press a key for another menu or screen.
4 Getting Started
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First Steps
Before starting the sample problems in this chapter, follow the steps on this
page to reset the TI.83 to its factory settings and clear all memory. This
ensures that the keystrokes in this chapter will produce the illustrated results.
To reset the TI.83, follow these steps.
1. Press É to turn on the calculator.
2. Press and release y, and then press
[MEM] (above Ã).
When you press y, you access the
operation printed in yellow above the next
key that you press. [MEM] is the
y operation of the à key.
The MEMORY menu is displayed.
3. Press 5 to select 5:Reset.
The RESET menu is displayed.
4. Press 1 to select 1:All Memory.
The RESET MEMORY menu is displayed.
5. Press 2 to select 2:Reset.
All memory is cleared, and the calculator
is reset to the factory default settings.
When you reset the TI.83, the display
contrast is reset.
¦
¦
If the screen is very light or blank, press
and release y, and then press and
hold } to darken the screen.
If the screen is very dark, press and
release y, and then press and hold †
to lighten the screen.
Getting Started 5
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Entering a Calculation: The Quadratic Formula
Use the quadratic formula to solve the quadratic equations 3X2 + 5X + 2 = 0
and 2X2 N X + 3 = 0. Begin with the equation 3X2 + 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 Ž) 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.
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 [‡] ƒ [B]
¡ ¹ 4 ƒ [A] ƒ [C] ¤ ¤ ¥ £ 2
ƒ [A] ¤ to enter the expression for
one of the solutions for the quadratic
formula,
2
−
b+ b −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.
6 Getting Started
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Converting to a Fraction: The Quadratic Formula
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.
To save keystrokes, you can recall the last expression you entered, and then
edit it for a new calculation.
4. Press y [ENTRY] (above Í) to recall
the fraction conversion entry, and then
press y [ENTRY] again to recall the
quadratic-formula expression,
2
−
b+ b −4ac
2a
5. Press } to move the cursor onto the + sign
in the formula. Press ¹ to edit the
quadratic-formula expression to become:
2
−
b− b −4ac
2a
6. Press Í to find the other solution for
the quadratic equation 3X2 + 5X + 2 = 0.
Getting Started 7
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Displaying Complex Results: The Quadratic Formula
Now solve the equation 2X2 N X + 3 = 0. When you set a+bi complex number
mode, the TI.83 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 [QUIT] (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.
4. Press y [ENTRY] to recall the store
instruction, and then press y [ENTRY]
again to recall the quadratic-formula
expression,
2
−
b− b −4ac
2a
5. Press Í to find one solution for the
equation 2X2 N X + 3 = 0.
6. Press y [ENTRY] repeatedly until this
quadratic-formula expression is displayed:
2
−
b+ b −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).
8 Getting Started
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Defining a Function: Box with Lid
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
From the diagram: 2X + A = 20
20
A
2X + 2B = 25
V = A B X
X
B
X
B
Substituting:
V = (20 N 2X) (25à 2 N X) X
25
1. Press o to display the Y= editor, which is
where you define functions for tables and
graphing.
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.
Getting Started 9
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Defining a Table of Values: Box with Lid
The table feature of the TI.83 displays numeric information about a function.
You can use a table of values from the function defined on page 9 to estimate
an answer to the problem.
1. Press y [TBLSET] (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.
4. Press y [TABLE] (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 [TBLSET].
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.)
10 Getting Started
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Zooming In on the Table: Box with Lid
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 [TABLE].
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.
4. Press y [TBLSET]. Press 3 Ë 6 Í to
set TblStart. Press Ë 01 Í to set @Tbl.
5. Press y [TABLE], and then press † and }
to scroll the table.
Four equivalent maximum values are
shown, 410.60 at X=3.67, 3.68, 3.69, and
3.70.
6. Press † and } 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.
7. Press † to display the other maximums.
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-cm. increments.
Getting Started 11
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Setting the Viewing Window: Box with Lid
You also can use the graphing features of the TI.83 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.
The standard window variables define the
Ymax
viewing window as shown. Xmin, Xmax,
Ymin, and Ymax define the boundaries of
Xscl
Xmin
the display. Xscl and Yscl define the
Xmax
distance between tick marks on the X and
Yscl
Y axes. Xres controls resolution.
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.
12 Getting Started
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Displaying and Tracing the Graph: Box with Lid
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.
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.
Getting Started 13
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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.
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.
14 Getting Started
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Zooming In on the Graph: Box with Lid
To help identify maximums, minimums, roots, and intersections of functions,
you can magnify the viewing window at a specific location using the ZOOM
instructions.
1. Press q to display the ZOOM menu.
This menu is a typical TI.83 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 (as in step 8 on page 14),
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.
4. Press p to display the new window
settings.
Getting Started 15
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Finding the Calculated Maximum: Box with Lid
You can use a CALCULATE menu operation to calculate a local maximum of a
function.
1. Press y [CALC] (above r) to display
the CALCULATE menu. Press 4 to select
4:maximum.
The graph is displayed again with a
Left Bound? prompt.
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.
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.
16 Getting Started
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Other TI-83 Features
Getting Started has introduced you to basic TI.83 operation. This guidebook
describes in detail the features you used in Getting Started. It also covers the
other features and capabilities of the TI.83.
Graphing
You can store, graph, and analyze up to 10 functions
(Chapter 3), up to six parametric functions (Chapter 4), up
to six polar functions (Chapter 5), and up to three
sequences (Chapter 6). You can use DRAW operations to
annotate graphs (Chapter 8).
Sequences
You can generate sequences and graph them over time. Or,
you can graph them as web plots or as phase plots
(Chapter 6).
Tables
You can create function evaluation tables to analyze many
functions simultaneously (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 (Chapter 9).
Matrices
Lists
You can enter and save up to 10 matrices and perform
standard matrix operations on them (Chapter 10).
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 (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 (Chapter 12).
Getting Started 17
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Inferential
Statistics
You can perform 16 hypothesis tests and confidence
intervals and 15 distribution functions. You can display
hypothesis test results graphically or numerically
(Chapter 13).
Financial
Functions
You can use time-value-of-money (TVM) functions to
analyze financial instruments such as annuities, 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 (Chapter 14).
CATALOG
The CATALOG is a convenient, alphabetical list of all
functions and instructions on the TI.83. You can paste any
function or instruction from the CATALOG to the current
cursor location (Chapter 15).
Programming
You can enter and store programs that include extensive
control and input/output instructions (Chapter 16).
Communication
Link
The TI.83 has a port to connect and communicate with
another TI.83, a TI.82, the Calculator-Based Laboratoryé
(CBL 2é, CBLé) System, a Calculator-Based Rangeré
(CBRé), or a personal computer. The unit-to-unit link
cable is included with the TI.83 (Chapter 19).
18 Getting Started
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the TI-83
1
Contents
Turning On and Turning Off the TI.83.................... 1-2
Setting the Display Contrast ............................. 1-3
The Display.............................................. 1-4
Entering Expressions and Instructions................... 1-6
TI.83 Edit Keys .......................................... 1-8
Setting Modes ........................................... 1-9
Using TI.83 Variable Names ............................. 1-13
Storing Variable Values .................................. 1-14
Recalling Variable Values ................................ 1-15
ENTRY (Last Entry) Storage Area........................ 1-16
Ans (Last Answer) Storage Area ......................... 1-18
TI.83 Menus ............................................. 1-19
VARS and VARS Y.VARS Menus......................... 1-21
Equation Operating System (EOSé) ..................... 1-22
Error Conditions......................................... 1-24
Operating the TI-83 1-1
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Turning On and Turning Off the TI-83
Turning On the
Calculator
To turn on the TI.83, press É.
•
If you previously had turned off the calculator by
pressing y [OFF], the TI.83 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 will return exactly as
you left it, including the display, cursor, and any error.
To prolong the life of the batteries, APD turns off the TI.83
automatically after about five minutes without any activity.
Turning Off the
Calculator
To turn off the TI.83 manually, press y [OFF].
•
•
All settings and memory contents are retained by
Constant Memoryé.
Any error condition is cleared.
Batteries
The TI.83 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.
1-2 Operating the TI-83
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Setting the Display Contrast
Adjusting the
You can adjust the display contrast to suit your viewing
Display Contrast 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 has 40 contrast settings, so each number 0 through 9
represents four settings.
The TI.83 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.
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 When the batteries are low, a low-battery message is
Batteries
displayed when you turn on the calculator.
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 will turn off
automatically and the unit will not operate. Batteries must
be replaced. All memory is retained.
Note: The operating period following the first low-battery message
could be longer than two weeks if you use the calculator infrequently.
Operating the TI-83 1-3
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The Display
Types of
Displays
The TI.83 displays both text and graphs. Chapter 3
describes graphs. Chapter 9 describes how the TI.83 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. 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 screen can display a
maximum of eight 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.
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 interprets
expressions and displays answers (page 1.9).
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 scroll the answer.
Entry
Answer
Returning to the
Home Screen
To return to the home screen from any other screen, press
y [QUIT].
Busy Indicator
When the TI.83 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.
1-4 Operating the TI-83
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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
Entry
Effect of Next Keystroke
Solid rectangle A character is entered at the
$
cursor; any existing character is
overwritten
Insert Underline
A character is inserted in front of
the cursor location
__
Second Reverse arrow A 2nd character (yellow on the
Þ
keyboard) is entered or a 2nd
operation is executed
Alpha Reverse A
An alpha character (green on the
keyboard) is entered or SOLVE is
executed
Ø
Full
Checkerboard No entry; the maximum characters
rectangle
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
underline cursor becomes an underlined # ( # ).
Graphs and editors sometimes display additional cursors,
which are described in other chapters.
Operating the TI-83 1-5
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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,
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 evaluated according to
Equation Operating System (EOSé) rules (page 1.22), and
the answer is displayed.
Most TI.83 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 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 [‡] 5 ¤ ¤
à 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 entry (ENTRY; page 1.16).
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Entering a
Number in
Scientific
Notation
To enter a number in scientific notation, follow these
steps.
1. Enter the part of the number that precedes the
exponent. This value can be an expression.
2. Press y [EE]. 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
does not automatically display answers in scientific or
engineering notation. The mode settings (page 1.9) and the
size of the number determine the display format.
Functions
A function returns a value. For example, ÷, L, +, ‡(, and log(
are the functions in the example on page 1.6. In general, the
first letter of each function is lowercase on the TI.83. Most
functions take at least one argument, as indicated by an open
parenthesis ( ( ) following the name. For example, sin(
requires one argument, sin(value).
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
would be indicated by the busy indicator, press É.
When you interrupt a calculation, the 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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TI-83 Edit Keys
Keystrokes Result
~ or |
Moves the cursor within an expression; these keys repeat.
} or †
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 [INS]
Changes the cursor to __ ; inserts characters in front of the
underline cursor; to end insertion, press y [INS] or press |, },
~, or †.
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 [A.LOCK] Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes
(on an alpha key) paste alpha characters; to cancel alpha-lock,
press ƒ; name prompts set alpha-lock 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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Setting Modes
Checking Mode
Settings
Mode settings control how the TI.83 displays and
interprets numbers and graphs. Mode settings are retained
by the Constant Memory feature when the TI.83 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 Number of decimal places
Radian Degree Unit of angle measure
Func Par Pol Seq Type of graphing
Numeric notation
Connected
Dot
Whether to connect graph points
Sequential
Simul Whether to plot simultaneously
Real a+bi re^qi
Full Horiz G-T
Real, rectangular cplx, or polar cplx
Full screen, two split-screen modes
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 command line, select the mode setting from
the mode screen; the instruction is pasted to the cursor
location.
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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.
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 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.
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)
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Radian, Degree
Angle modes control how the TI.83 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.
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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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 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.
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).
1-12 Operating the TI-83
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Using TI-83 Variable Names
Variables and
Defined Items
On the TI.83 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 uses assigned names for variables and other
items saved in memory. For lists, you also can create your
own five-character names.
Variable Type
Real numbers
Complex numbers
Matrices
Names
A, B, . . . , Z, q
A, B, . . . , Z, q
ãAä, ãBä, ãCä, . . . , ãJä
Lists
L1, L2, L3, L4, L5, L6, and user-
defined names
Functions
Y1, Y2, . . . , Y9, Y0
Parametric equations X1T and Y1T, . . . , X6T and Y6T
Polar functions
Sequence functions
Stat plots
r1, r2, r3, r4, r5, r6
u, v, w
Plot1, Plot2, Plot3
Graph databases
Graph pictures
Strings
GDB1, GDB2, . . . , GDB9, GDB0
Pic1, Pic2, . . . , Pic9, Pic0
Str1, Str2, . . . , Str9, Str0
Xmin, Xmax, and others
System variables
•
•
•
You can create as many list names as memory will allow
Notes about
Variables
(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.
You can use DRAW STO menu items to store and recall
graph databases and pictures (Chapter 8).
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Storing Variable Values
Storing Values in Values are stored to and recalled from memory using
a Variable
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.
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.
1-14 Operating the TI-83
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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 Ž, 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).
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.
Operating the TI-83 1-15
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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, ENTRY is retained in
memory.
To recall ENTRY, press y [ENTRY]. 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 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 [ENTRY]
Accessing a
Previous Entry
The TI.83 retains as many previous entries as possible in
ENTRY, up to a capacity of 128 bytes. To scroll those
entries, press y [ENTRY] 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 [ENTRY]
If you press y [ENTRY] after displaying the oldest stored
entry, the newest stored entry is displayed again, then the
next-newest entry, and so on.
y [ENTRY]
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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.
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
To store to ENTRY two or more expressions or
Values on a Line 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 [ENTRY], 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.
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 [p] ƒ R ¡ Í
y [ENTRY]
y | 7 y [INS] 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 is
holding in the ENTRY storage area.
Operating the TI-83 1-17
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Ans (Last Answer) Storage Area
Using Ans in an
Expression
When an expression is evaluated successfully from the
home screen or from a program, the TI.83 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, the value in Ans is retained in
memory.
You can use the variable Ans to represent the last answer in
most places. Press y [ANS] to copy the variable name Ans
to the cursor location. When the expression is evaluated, the
TI.83 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 [ANS]
Í
Continuing an
Expression
You can use Ans as the first entry in the next expression
without entering the value again or pressing y [ANS]. On
a blank line on the home screen, enter the function. The
TI.83 pastes the variable name Ans to the screen, then the
function.
5 ¥ 2
Í
¯ 9 Ë 9
Í
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 [p] 5 ¡
Í
¯ 3 Ë 3
Í
¿ ƒ V
Í
1-18 Operating the TI-83
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TI-83 Menus
Using a TI-83
Menu
You can access most TI.83 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.
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.
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 †.
Operating the TI-83 1-19
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Selecting an Item You can select an item from a menu in either of two ways.
from a Menu
•
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 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, then the cursor moves beyond it to the next
item.
Calculate 3‡27.
† † † Í
27 ¤ Í
Leaving a Menu
You can leave a menu without making a selection in any of
without Making a four ways.
Selection
•
•
•
Press y [QUIT] 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 [LIST].
•
Press a key or key combination for a different screen,
such as o or y [TABLE].
1-20 Operating the TI-83
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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...
2:Zoom...
3:GDB...
4:Picture...
5:Statistics...
6:Table...
7:String...
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
String variables
Selecting a
To display the VARS Y.VARS menu, press ~.
Variable from the 1:Function, 2:Parametric, and 3:Polar display secondary
VARS Menu or
VARS Y-VARS
Menu
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.
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.
Operating the TI-83 1-21
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Equation Operating System (EOS™)
Order of
Evaluation
The Equation Operating System (EOSé) defines the order
in which functions in expressions are entered and
evaluated on the TI.83. EOS lets you enter numbers and
functions in a simple, straightforward sequence.
EOS evaluates the functions in an expression in this order:
1
2
Single-argument functions that precede the
argument, such as ‡(, sin(, or log(
Functions that are entered after the argument,
such as 2, M1, !, ¡, , and conversions
r
x
3
4
5
Powers and roots, such as 2^5 or 5 ‡32
Permutations (nPr) and combinations (nCr)
Multiplication, implied multiplication, and
division
6
7
8
9
Addition and subtraction
Relational functions, such as > or
Logic operator and
Logic operators or and xor
Within a priority level, EOS evaluates functions from left to
right.
Calculations within parentheses are evaluated first.
2
Multiargument functions, such as nDeriv(A ,A,6), are
evaluated as they are encountered.
1-22 Operating the TI-83
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Implied
Multiplication
The TI.83 recognizes implied multiplication, so you need
not press ¯ to express multiplication in all cases. For
example, the TI.83 interprets 2p, 4sin(46), 5(1+2), and (2ä5)7
as implied multiplication.
Note: TI.83 implied multiplication rules differ from those of the TI.82.
For example, the TI.83 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.
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, 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).
Operating the TI-83 1-23
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Error Conditions
Diagnosing an
Error
The TI.83 detects errors while performing these tasks.
•
•
•
•
Evaluating an expression
Executing an instruction
Plotting a graph
Storing a value
When the TI.83 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 [QUIT] 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.
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.
1-24 Operating the TI-83
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Math, Angle, and Test
Operations
2
Contents
Getting Started: Coin Flip................................ 2-2
Keyboard Math Operations .............................. 2-3
MATH Operations........................................ 2-5
Using the Equation Solver ............................... 2-8
MATH NUM (Number) Operations........................ 2-13
Entering and Using Complex Numbers................... 2-16
MATH CPX (Complex) Operations ....................... 2-18
MATH PRB (Probability) Operations ..................... 2-20
ANGLE Operations....................................... 2-23
TEST (Relational) Operations............................ 2-24
TEST LOGIC (Boolean) Operations ...................... 2-26
Math, Angle, and Test Operations 2-1
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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 ¤.
2. Press Í to evaluate the expression. A
list of 40 elements is 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 ¿ 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).
4. Press ~ or | to view the additional counts
in the list. Ellipses (...) indicate that the list
continues beyond the screen.
Note: Since randBin( generates random
numbers, your list elements may differ from those
in the example.
2-2 Math, Angle, and Test Operations
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Keyboard Math Operations
Using Lists with
Math operations that are valid for lists return a list
Math Operations calculated element by element. If you use two lists in the
same expression, they must be the same length.
+ (Addition),
N (Subtraction),
You can use + (addition, Ã), N (subtraction, ¹), ä
(multiplication, ¯), and à (division, ¥) with real and
ä (Multiplication), complex numbers, expressions, lists, and matrices. You
à (Division)
cannot use à with matrices.
valueA+valueB
valueAävalueB
valueA N valueB
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.
sin(value)
cos(value)
tan(value)
L1
You can use the inverse trig functions (arcsine, y [SIN ];
L1
L1
arccosine, y [COS ]; and arctangent, y [TAN ]) 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),
You can use ^ (power, ›), 2 (square, ¡), and ‡( (square
root, y [‡]) with real and complex numbers, expressions,
‡( (Square Root) lists, and matrices. You cannot use ‡( with matrices.
value^power
value2
‡(value)
1 (Inverse)
L
You can use L1 (inverse, —
) with real and complex
numbers, expressions, lists, and matrices. The
multiplicative inverse is equivalent to the reciprocal, 1àx.
valueL1
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log(,
10^(,
ln(
You can use log( (logarithm, «), 10^( (power of 10, y
[10 ]), and ln( (natural log, µ) with real or complex
numbers, expressions, and lists.
x
log(value)
10^(power)
ln(value)
x
e^( (Exponential) e^( (exponential, y ãe ]) 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.
Press y [e] to copy e to the cursor location. In
calculations, the TI-83 uses 2.718281828459 for e.
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
2
evaluated. For example, LA returns a negative number,
because squaring is evaluated before negation. Use
2
parentheses to square a negated number, as in (LA) .
Note: On the TI-83, 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 [p]) is stored as a constant in the TI-83. In
calculations, the TI-83 uses 3.1415926535898 for p.
2-4 Math, Angle, and Test Operations
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MATH Operations
MATH Menu
To display the MATH menu, press .
MATH NUM CPX PRB
1:4Frac
Displays the answer as a fraction.
2:4Dec
Displays the answer as a decimal.
Calculates the cube.
Calculates the cube root.
Calculates the xth root.
3
3:
4: ‡(
3
x
5:
‡
6:fMin(
7:fMax(
8:nDeriv(
9:fnInt(
0:Solver...
Finds the minimum of a function.
Finds the maximum of a function.
Computes the numerical derivative.
Computes the function integral.
Displays the equation 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.
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
Math, Angle, and Test Operations 2-5
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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
3
‡( (cube root) returns the cube root of value. You can use
‡( with real or complex numbers, expressions, and lists.
3
3
‡(value)
x
x‡ (Root)
‡ (xth root) returns the xth root of value. You can use x‡
with real or complex numbers, expressions, and lists.
xthrootx‡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+H)Nf(xNH)
f¢(x) =
2H
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 can return a
false derivative value at a nondifferentiable point.
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.
Math, Angle, and Test Operations 2-7
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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 (see step 3 picture on page
2.9) is displayed when an equation is stored in eqn.
Entering an
To enter an expression in the equation solver, assuming
Expression in the that the variable eqn is empty, follow these steps.
Equation Solver
1. Select 0:Solver from the MATH menu to display the
equation editor.
2. Enter the expression in any of three ways.
•
•
•
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 [RCL], 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.
2-8 Math, Angle, and Test Operations
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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}).
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.
Math, Angle, and Test Operations 2-9
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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 will attempt to display the solution that
is closest to your guess.
(upper+lower)
The default guess is calculated as
.
2
2-10 Math, Angle, and Test Operations
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4. Edit bound={lower,upper}. lower and upper are the
bounds between which the TI-83 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 [SOLVE] (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.
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.
Math, Angle, and Test Operations 2-11
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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 (page 2.10) or new bounds
(page 2.11) 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 [SOLVE].
Controlling the
Solution for
Solver or solve(
The TI-83 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 function solve( is available only from CATALOG or
the Home Screen from within a program. It returns a solution (root) of
or from a
Program
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.
2-12 Math, Angle, and Test Operations
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MATH NUM (Number) Operations
MATH NUM Menu To display the MATH NUM menu, press ~.
MATH NUM CPX PRB
1:abs(
Absolute value
Round
Integer part
Fractional part
Greatest integer
Minimum value
Maximum value
Least common multiple
Greatest common divisor
2:round(
3:iPart(
4:fPart(
5:int(
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.
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])
Math, Angle, and Test Operations 2-13
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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)
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.
2-14 Math, Angle, and Test Operations
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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.
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)
min(listA,listB)
min(list,value)
max(valueA,valueB)
max(list)
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.
lcm(valueA,valueB)
lcm(listA,listB)
lcm(list,value)
gcd(valueA,valueB)
gcd(listA,listB)
gcd(list,value)
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Entering and Using Complex Numbers
Complex-Number The TI-83 displays complex numbers in rectangular form
Modes
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, 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.
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 converts all entered trig
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.
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Interpreting
Complex numbers in results, including list elements, are
Complex Results displayed in either rectangular or polar form, as specified
by the mode setting or by a display conversion instruction
(page 2.19). In the example below, 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 [i] (constant).
real component(+ or N)imaginary componenti
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
x
of r (magnitude), press y [e ] (exponential function),
enter the value of q (angle), press y [i] (constant), and
then press ¤.
magnitudee^(anglei)
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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.
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).
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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).
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).
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MATH PRB (Probability) Operations
MATH PRB Menu To display the MATH PRB menu, press |.
MATH NUM CPX PRB
1:rand
2:nPr
3:nCr
4:!
Random-number generator
Number of permutations
Number of combinations
Factorial
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, randä5 generates a
random number > 0 and < 5.
With each rand execution, the TI-83 generates the same
random-number sequence for a given seed value. The TI-83
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 (page 2.22).
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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.
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.)
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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])
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 (page 2-20).
2-22 Math, Angle, and Test Operations
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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’s
interpretation of ANGLE menu entries.
ANGLE
1:¡
Degree notation
2:'
3:
DMS minute notation
Radian notation
r
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(
DMS 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"
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 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].
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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.
valuer
Degree mode
8DMS
8DMS (degree/minute/second) displays answer in DMS
format (page 2.23). 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
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.
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TEST (Relational) Operations
TEST Menu
To display the TEST menu, press y [TEST].
This operator...
Returns 1 (true) if...
TEST LOGIC
1:=
Equal
2:ƒ
Not equal to
3:>
Greater than
4:‚
5:<
Greater than or equal to
Less than
6:
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.
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 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 performs
the relational test first because it is in parentheses, and
then it adds 2, 1, and 3.
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TEST LOGIC (Boolean) Operations
TEST LOGIC
Menu
To display the TEST LOGIC menu, press y ãTESTä ~.
This operator...
Returns a 1 (true) if...
TEST LOGIC
1:and
2:or
3:xor
4:not(
Both values are nonzero (true).
At least one value is nonzero (true).
Only one value is zero (false).
The value is zero (false).
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.
valueA and valueB
valueA or valueB
valueA xor valueB
valueA valueB
and
1
or
1
xor
0
ƒ0
ƒ0
0
ƒ0
0
returns
returns
returns
returns
0
1
1
ƒ0
0
0
1
1
0
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.
2-26 Math, Angle, and Test Operations
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Function
3
Contents
Getting Started: Graphing a Circle ....................... 3-2
Defining Graphs ......................................... 3-3
Setting the Graph Modes................................. 3-4
Defining Functions ...................................... 3-5
Selecting and Deselecting Functions..................... 3-7
Setting Graph Styles for Functions....................... 3-9
Setting the Viewing Window Variables ................... 3-11
Setting the Graph Format ................................ 3-13
Displaying Graphs ....................................... 3-15
Exploring Graphs with the Free-Moving Cursor.......... 3-17
Exploring Graphs with TRACE........................... 3-18
Exploring Graphs with the ZOOM Instructions........... 3-20
Using ZOOM MEMORY .................................. 3-23
Using the CALC (Calculate) Operations .................. 3-25
Function Graphing 3-1
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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, 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.
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.
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Defining Graphs
TI-83—Graphing Chapter 3 specifically describes function graphing, but the
Mode Similarities steps shown here are similar for each TI-83 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
(page 3.4).
2. Press o and enter, edit, or select one or more functions
in the Y= editor (page 3.5 and 3.7).
3. Deselect stat plots, if necessary (page 3.7).
4. Set the graph style for each function (page 3.9).
5. Press p and define the viewing window variables
(page 3.11).
6. Press y [FORMAT] and select the graph format settings
(page 3.13).
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 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.
Function Graphing 3-3
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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 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.
•
•
•
•
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.
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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.
•
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.
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Defining a
To define a function from the home screen or a program,
begin on a blank line and follow these steps.
Function from
the Home Screen
or a Program
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.
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 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})
3-6 Function Graphing
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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 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.
Turning On or
To view and change the on/off status of a stat plot in the
Turning Off a Stat Y= editor, use Plot1 Plot2 Plot3 (the top line of the
Plot in the Y=
Editor
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.
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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.
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.
3-8 Function Graphing
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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 a*bove 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 A circular cursor traces the leading edge of
the graph without drawing a path
í
Dot
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.
Setting the Graph To set the graph style for a function, follow these steps.
Style
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 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.
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)
4 = ê (below)
(animate)
2 = è (thick)
5 = ë (path)
7 = í (dot)
3 = é (above)
6 = ì
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 Viewing The viewing window is the portion of the coordinate plane
Window
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.
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 to draw graphs more slowly.
Changing a
To change a window variable value from the window
Window Variable editor, follow these steps.
Value
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 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
To store a value, which can be an expression, to a window
Window Variable variable, begin on a blank line and follow these steps.
from the Home
Screen or a
1. Enter the value you want to store.
Program
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.
When the instruction is executed, the TI-83 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 [FORMAT]. 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.
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.
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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.
GridOff, GridOn
Grid points cover the viewing window in rows that
correspond to the tick marks (page 3.11) 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.
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 To display the graph of the selected function or functions,
Graph
press s. TRACE, ZOOM instructions, and CALC
operations display the graph automatically. As the TI-83
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 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.
If you performed any of these actions since the graph was
last displayed, the TI-83 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
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Overlaying
Functions on a
Graph
On the TI-83, 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.
Graphing a
If you enter a list (Chapter 11) as an element in an
Family of Curves expression, the TI-83 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 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
(page 3.18).
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 ZoomIn) 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 press y | or y
(Xres affects this), ~.
. . . to any valid X value on a function, enter a value, and
then press Í.
. . . from one function to another,
press } or †.
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 To move the trace cursor from function to function, press
Cursor from
Function to
Function
† 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.
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Moving the Trace To move the trace cursor to any valid X value on the
Cursor to Any
Valid X Value
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 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.
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
(page 3.15).
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
2:Zoom In
Draws a box to define the viewing window.
Magnifies the graph around the cursor.
3:Zoom Out Views more of a graph around the cursor.
4:ZDecimal Sets @X and @Y to 0.1.
5:ZSquare
Sets equal-size pixels on the X and Y axes.
6:ZStandard Sets the standard window variables.
Sets the built-in trig window variables.
7:ZTrig
8:ZInteger Sets integer values on the X and Y axes.
9:ZoomStat Sets the values for current stat lists.
0:ZoomFit
Fits YMin and YMax between XMin and XMax.
Zoom Cursor
ZBox
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 (+).
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.
To use ZBox to define another box within the new graph,
repeat steps 2 through 4. To cancel ZBox, press ‘.
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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 (page 3.24); 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.
4. Press Í. The TI-83 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
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.
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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
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
ZoomFit
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 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.
3:ZoomRcl
4:SetFactors... Changes Zoom In and Zoom Out factors.
ZPrevious
ZoomSto
ZPrevious replots the graph using the window variables of
the graph that was displayed before you executed the last
ZOOM instruction.
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.
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.
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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.
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
2:zero
3:minimum
4:maximum
Calculates a function Y value for a given X.
Finds a zero (x-intercept) of a function.
Finds a minimum of a function.
Finds a maximum of a function.
5:intersect Finds an intersection of two functions.
6:dy/dx
7:‰f(x)dx
Finds a numeric derivative of a function.
Finds a numeric integral of a function.
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.
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 ~.
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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.
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.
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 ~.
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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 (steps 2 through 4; page 3.26).
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.
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 †.
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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.
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 (step 3; page 3.26). 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.
3-28 Function Graphing
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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.
Horizontal:
Vertical:
X1(t)=tv0cos(q)
Y1(t)=tv0sin(q)N 12 gt2
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector:
X2(t)=0
Y2(t)=Y1(t)
Y3(t)=0
Horizontal vector: X3(t)=X1(t)
Gravity constant: g=9.8 m/sec2
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
[ANGLE] 1 (to select ¡) ¤ Í to define
X1T in terms of T.
3. Press 30 „ ˜ 25 y [ANGLE] 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.
4-2 Parametric Graphing
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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 [FORMAT] † † † ~ Í to set
AxesOff, which turns off the axes.
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.
Parametric Graphing 4-3
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Defining and Displaying Parametric Graphs
TI-83 Graphing
The steps for defining a parametric graph are similar to the
Mode Similarities 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.
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.
4-4 Parametric Graphing
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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.
Selecting and
Deselecting
Parametric
Equations
The TI-83 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... Largest T value to evaluate (2p)
Tstep=.1308996... T value increment (pà24)
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
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 To display the current graph format settings, press y
Format
[FORMAT]. 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 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.
•
Store parametric equations.
•
•
Select or deselect parametric equations.
Store values directly to window variables.
4-6 Parametric Graphing
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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.
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).
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Moving the Trace To move the trace cursor to any valid T value on the
Cursor to Any
Valid T Value
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.
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.
4-8 Parametric Graphing
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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.
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 [p] 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.
5-2 Polar Graphing
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Defining and Displaying Polar Graphs
TI-83 Graphing
The steps for defining a polar graph are similar to the steps
Mode Similarities 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.
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 (page 5.4).
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.
Polar Graphing 5-3
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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
The TI-83 graphs only the selected polar equations. In the
Deselecting Polar Y= editor, a polar equation is selected when the = sign is
Equations
highlighted. You may select any or all of the equations.
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
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
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
Note: To ensure that sufficient points are plotted, you may want to
change the q window variables.
5-4 Polar Graphing
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Setting the Graph To display the current graph format settings, press y
Format
[FORMAT]. 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 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.
Store polar equations.
Select or deselect polar equations.
Store values directly to window variables.
Polar Graphing 5-5
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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 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 To move the trace cursor to any valid q value on the
Cursor to Any
Valid q Value
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.
CALC
CALC operations in Pol graphing work the same as in Func
graphing. The CALCULATE menu items available in Pol
graphing are 1:value, 2:dy/dx, and 3:dr/dq.
5-6 Polar Graphing
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Sequence
6
Contents
Getting Started: Forest and Trees ........................ 6-2
Defining and Displaying Sequence Graphs ............... 6-3
Selecting Axes Combinations ............................ 6-8
Exploring Sequence Graphs.............................. 6-9
Graphing Web Plots...................................... 6-11
Using Web Plots to Illustrate Convergence............... 6-12
Graphing Phase Plots .................................... 6-13
Comparing TI-83 and TI.82 Sequence Variables.......... 6-15
Keystroke Differences Between TI-83 and TI-82 ......... 6-16
Sequence Graphing 6-1
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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 [FORMAT] and select Time axes
format and ExprOn format if necessary.
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
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?
6-2 Sequence Graphing
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Defining and Displaying Sequence Graphs
TI-83 Graphing
The steps for defining a sequence graph are similar to the
Mode Similarities 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 To display the mode screen, press z. To graph
Graphing Mode
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 Sequence
Functions u, v,
and w
The TI-83 has three sequence functions that you can enter
from the keyboard: u, v, and w. They are above the ¬, −,
and ® keys.
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).
Sequence Graphing 6-3
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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.
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
The TI-83 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.
Functions
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).
6-4 Sequence Graphing
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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 [CATALOG] [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.
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.
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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).
Using an initial value u(nMin) = 1, the sequence above
returns 1, 2, 4, 8, 16, . . .
Tip: On the TI-83, 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).
6-6 Sequence Graphing
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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
Ymin=L10
Ymax=10
Yscl=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
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).
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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Selecting Axes Combinations
Setting the Graph To display the current graph format settings, press y
Format
[FORMAT]. 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 Web uv 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.
Axes Setting
x-axis
n
y-axis
Time
Web
uv
u(n), v(n), w(n)
u(nN1), v(nN1), w(nN1) u(n), v(n), w(n)
u(n)
v(n)
u(n)
v(n)
w(n)
w(n)
vw
uw
See pages 6.11 and 6.12 for more information on Web
plots. See page 6.13 for more information on phase plots
(uv, vw, and uw axes settings).
Displaying a
To plot the selected sequence functions, press s. As a
Sequence Graph graph is plotted, the TI-83 updates X, Y, and n.
Smart Graph applies to sequence graphs (Chapter 3).
6-8 Sequence Graphing
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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.
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 To move the trace cursor to any valid n value on the
Cursor to Any
Valid n Value
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.
Sequence Graphing 6-9
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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).
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.
6-10 Sequence Graphing
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Graphing Web Plots
Graphing a Web
Plot
To select Web axes format, press y [FORMAT] ~ 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.
Displaying the
Graph Screen
In Web format, press s to display the graph screen.
The TI-83:
•
•
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 ~.
Sequence Graphing 6-11
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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 [FORMAT] 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
4. Press s to graph the sequence.
5. Press y [FORMAT] 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.
6-12 Sequence Graphing
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Graphing Phase Plots
Graphing with uv, The phase-plot axes settings uv, vw, and uw show
vw, and uw
relationships between two sequences. To select a
phase-plot axes setting, press y [FORMAT], press ~ until
the cursor is on uv, vw, or uw, and then press Í.
Axes Setting
x-axis
u(n)
y-axis
v(n)
uv
vw
uw
v(n)
w(n)
w(n)
u(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 wolves and rabbits, with initial populations
of 200 rabbits (u(nMin)) and 50 wolves (v(nMin)).
These are the variables (given values are in parentheses):
R
M
K
W
G
D
n
= number of rabbits
= rabbit population growth rate without wolves (.05)
= rabbit population death rate with wolves
= number of wolves
= wolf population growth rate with rabbits
= wolf population death rate without rabbits
= time (in months)
(.001)
(.0002)
(.03)
Rn = RnN1(1+MNKWnN1
)
Wn = WnN1(1+GRnN1ND)
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).
Sequence Graphing 6-13
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2. Press y [FORMAT] Í to select Time axes format.
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 wolves (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 [FORMAT] ~ ~ Í to select uv axes
format.
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 wolves (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.
6-14 Sequence Graphing
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Comparing TI-83 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 sequences and sequence window variables, as
well as their TI-82 counterparts.
TI.83
TI.82
In the Y= editor:
u(n)
Un
u(nMin)
v(n)
UnStart (window variable)
Vn
v(nMin)
VnStart (window variable)
not available
w(n)
w(nMin)
In the window editor:
nMin
not available
nStart
nMax
nMax
PlotStart
PlotStep
nMin
not available
Sequence Graphing 6-15
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Keystroke Differences Between TI-83 and TI-82
Sequence
Keystroke
Changes
Refer to the table if you are familiar with the TI-82. It
compares TI-83 sequence-name syntax and variable syntax
with TI.82 sequence-name syntax and variable syntax.
TI.83 / TI.82
n / n
On TI.83, press:
On TI.82, press:
y [n]
„
u(n) / Un
y [u]
£ „ ¤
y [Y.VARS] ¶ À
v(n) / Vn
y [v]
£ „ ¤
y [Y.VARS] ¶ Á
w(n)
y [w]
£ „ ¤
not available
u(nN1) / UnN1
v(nN1) / VnN1
w(nN1)
y [u]
y [UnN1
y [VnN1
not available
]
£ „ ¹ À ¤
y [v]
£ „ ¹ À ¤
]
y [w]
£ „ ¹ À ¤
6-16 Sequence Graphing
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Tables
7
Contents
Getting Started: Roots of a Function ..................... 7-2
Setting Up the Table ..................................... 7-3
Defining the Dependent Variables........................ 7-4
Displaying the Table ..................................... 7-5
Tables 7-1
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Getting Started: Roots of a Function
Getting Started is a fast-paced introduction. Read the chapter for details.
Evaluate the function Y = X3 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.
3
2. Press o. Press „ 3 to select .
Then press ¹ 2 „ to enter the
3
function Y1=X N2X.
3. Press y [TBLSET] to display the TABLE
SETUP screen. Press Ì 10 Í to set
TblStart=L10. Press 1 Í to set @Tbl=1.
Press Í to select Indpnt: Auto
(automatically generated independent
values). Press † Í to select
Depend: Auto (automatically generated
dependent values).
4. Press y [TABLE] 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?
7-2 Tables
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Setting Up the Table
TABLE SETUP
Screen
To display the TABLE SETUP screen, press y [TBLSET].
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.
Indpnt: Auto,
Indpnt: Ask,
Depend: Auto,
Depend: Ask
Selections
Table Characteristics
Indpnt: Auto
Values are displayed automatically in both
Depend: Auto the independent-variable column and in all
dependent-variable columns.
Indpnt: Ask
The table is empty; when you enter a value
Depend: Auto 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 [TBLSET] in the program editor, you
can select IndpntAuto, IndpntAsk, DependAuto, and
DependAsk.
Tables 7-3
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Defining the Dependent Variables
Defining
In the Y= editor, enter the functions that define the
Dependent
Variables from
the Y= Editor
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
To edit a selected Y= function from the table editor, follow
these steps.
Variables from
the Table Editor
1. Press y [TABLE] 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.
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.
7-4 Tables
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Displaying the Table
The Table
To display the table, press y [TABLE].
Current cell
Independent-
variable values
in the first
Dependent-
variable values in
the second and
third columns
column
Current cell’s full value
Note: The table abbreviates the values, if necessary.
Independent and The current graphing mode determines which independent
Dependent
Variables
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.
Graphing Mode
Func (function)
Par (parametric)
Independent
Variable
Dependent
Variable
X
Y1 through Y9, and
Y0
T
X1T/Y1T through
X6T/Y6T
Pol (polar)
q
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.
Tables 7-5
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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.
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 If you have defined more than two dependent variables,
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 on the table two dependent variables
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.
7-6 Tables
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Draw
Instructions
8
Contents
Getting Started: Drawing a Tangent Line................. 8-2
Using the DRAW Menu................................... 8-3
Clearing Drawings ....................................... 8-4
Drawing Line Segments.................................. 8-5
Drawing Horizontal and Vertical Lines ................... 8-6
Drawing Tangent Lines .................................. 8-8
Drawing Functions and Inverses......................... 8-9
Shading Areas on a Graph ............................... 8-10
Drawing Circles.......................................... 8-11
Placing Text on a Graph ................................. 8-12
Using Pen to Draw on a Graph ........................... 8-13
Drawing Points on a Graph .............................. 8-14
Drawing Pixels .......................................... 8-16
Storing Graph Pictures (Pics) ............................ 8-17
Recalling Graph Pictures (Pics) .......................... 8-18
Storing Graph Databases (GDBs) ........................ 8-19
Recalling Graph Databases (GDBs) ...................... 8-20
DRAW Instructions 8-1
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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 = sinX.
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.
3. Press y [DRAW] 5 to select 5:Tangent(.
The tangent instruction is initiated.
4. Press y [‡] 2 ¤ ¥ 2.
5. Press Í. The tangent line is drawn; the
X value and the tangent-line equation are
displayed on the graph.
8-2 DRAW Instructions
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Using the DRAW Menu
DRAW Menu
To display the DRAW menu, press y [DRAW]. The TI-83’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.
3:Horizontal Draws a horizontal line.
4:Vertical
5:Tangent(
6:DrawF
Draws a vertical line.
Draws a line segment tangent to a function.
Draws a function.
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
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 (page 8.4).
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.
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.
DRAW Instructions 8-3
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Clearing Drawings
Clearing
All points, lines, and shading drawn on a graph with DRAW
instructions are temporary.
Drawings When
a Graph Is
Displayed
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
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 Home Screen the program editor. Select 1:ClrDraw from the DRAW menu.
or a Program
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
(page 8.17).
8-4 DRAW Instructions
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Drawing Line Segments
Drawing a Line
To draw a line segment when a graph is displayed, follow
Segment Directly these steps.
on a Graph
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 ‘.
Drawing a Line
Segment from
Line( also draws a line segment between the coordinates
(X1,Y1) and (X2,Y2). The values may be entered as
the Home Screen expressions.
or a Program
Line(X1,Y1,X2,Y2)
To erase a line segment, enter Line(X1,Y1,X2,Y2,0)
DRAW Instructions 8-5
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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 ‘.
8-6 DRAW Instructions
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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 to draw more than one horizontal or
vertical line, separate each instruction with a colon ( : ).
DRAW Instructions 8-7
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Drawing Tangent Lines
Drawing
a Tangent Line
Directly
To draw a tangent line when a graph is displayed, follow
these steps.
1. Select 5:Tangent( from the DRAW menu.
on a Graph
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.
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
Tangent( (tangent line) draws a line tangent to expression
in terms of X, such as Y1 or X , at point X=value. X can be
an expression. expression is interpreted as being in Func
mode.
2
a Tangent Line
from the Home
Screen or
a Program
Tangent(expression,value)
8-8 DRAW Instructions
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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 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
returns to the home screen or the program editor. DrawInv
is not interactive. DrawInv works in Func mode only.
DrawInv expression
Note: You cannot use a list in expression to draw a family of curves.
DRAW Instructions 8-9
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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¡
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])
8-10 DRAW Instructions
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Drawing Circles
Drawing a Circle To draw a circle directly on a displayed graph using the
Directly on a
Graph
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.
To continue drawing circles, repeat steps 2 and 3. To
cancel Circle(, press ‘.
Drawing a Circle Circle( draws a circle with center (X,Y) and radius. These
from the Home
Screen or a
Program
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.
DRAW Instructions 8-11
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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 [A.LOCK] to
enter letters and q. You may enter TI-83 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 Text( places on the current graph the characters
Graph from the
Home Screen or
a Program
comprising value, which can include TI-83 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.
Text(row,column,value,value . . .)
value can be text enclosed in quotation marks ( " ), or it
can be an expression. The TI-83 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.
8-12 DRAW Instructions
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Using Pen to Draw on a Graph
Using Pen to
Pen draws directly on a graph only. You cannot execute
Draw on a Graph 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.
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 ‘.
DRAW Instructions 8-13
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Drawing Points on a Graph
DRAW POINTS
Menu
To display the DRAW POINTS menu, press y [DRAW] ~.
The TI-83’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.
3. Press Í to draw the point.
To continue drawing points, repeat steps 2 and 3. To
cancel Pt.On(, press ‘.
8-14 DRAW Instructions
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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 ‘.
Changing Points To change (toggle on or off) a point on a graph, follow
with Pt-Change(
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)
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.
DRAW Instructions 8-15
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Drawing Pixels
TI-83 Pixels
A pixel is a square dot on the TI-83 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
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)
Using pxl-Test(
Split Screen
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)
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(.
8-16 DRAW Instructions
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Storing Graph Pictures (Pics)
DRAW STO Menu To display the DRAW STO menu, press y [DRAW] |.
When you select an instruction from the DRAW STO menu,
the TI-83 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.
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 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.
DRAW Instructions 8-17
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Recalling Graph Pictures (Pics)
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 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 To delete graph pictures from memory, use the
Picture
MEMORY DELETE FROM menu (Chapter 18).
8-18 DRAW Instructions
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Storing Graph Databases (GDBs)
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.
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 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.
DRAW Instructions 8-19
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Recalling Graph Databases (GDBs)
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 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
changes the graphing mode automatically, if necessary.
Deleting a Graph To delete a GDB from memory, use the MEMORY DELETE
Database
FROM menu (Chapter 18).
8-20 DRAW Instructions
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Split
Screen
9
Contents
Getting Started: Exploring the Unit Circle................ 9-2
Using Split Screen ....................................... 9-3
Horiz (Horizontal) Split Screen .......................... 9-4
G.T (Graph-Table) Split Screen .......................... 9-5
TI-83 Pixels in Horiz and G.T Mode ...................... 9-6
Split Screen 9-1
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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 [FORMAT] to display the format
screen. Press † † † † † ~ Í to
select ExprOff.
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 Xmax=2.3
Tstep=15 Xscl=1
Xmin=L2.3
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.
9-2 Split Screen
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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.
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 [TABLE], the cursor is placed in
the half in which the table is displayed.
The TI-83 will remain in split-screen mode until you
change back to Full screen mode.
Split Screen 9-3
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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)
Moving from Half To use the top half of the split screen:
to Half in Horiz
Mode
•
•
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 [TABLE] (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.
9-4 Split Screen
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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 use the left half of the split screen:
to Half in G-T
Mode
•
•
Press s or r.
Select a ZOOM or CALC operation.
To use the right half of the split screen, press y [TABLE].
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.
Split Screen 9-5
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TI-83 Pixels in Horiz and G-T Modes
TI-83 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.
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
To set Horiz or G.T from a program, follow these steps.
Split-Screen
Mode from the
Home Screen or
a Program
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).
9-6 Split Screen
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Matrices
10
Contents
Getting Started: Systems of Linear Equations ............ 10-2
Defining a Matrix ........................................ 10-2
Viewing and Editing Matrix Elements.................... 10-4
Using Matrices with Expressions ........................ 10-7
Displaying and Copying Matrices ........................ 10-8
Using Math Functions with Matrices..................... 10-9
Using the MATRX MATH Operations ..................... 10-12
Matrices 10-1
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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, 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 Ž. 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.
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 [QUIT] to return to the home
screen. If necessary, press ‘ to clear
the home screen. Press Ž ~ 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 Ž 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 so X = L3 + Z
1Y + 2Z = 3
so Y = 3 N 2Z
10-2 Matrices
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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 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 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 Ž | to display the MATRX EDIT menu. The
dimensions of any previously defined matrices are
displayed.
2. Select the matrix you want to define. The MATRX EDIT
screen is displayed.
Accepting or
The dimensions of the matrix (row × column) are
Changing Matrix displayed on the top line. The dimensions of a new matrix
Dimensions
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.
Matrices 10-3
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Viewing and Editing Matrix Elements
Displaying Matrix After you have set the dimensions of the matrix, you can
Elements
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.
Deleting a Matrix To delete matrices from memory, use the MEMORY DELETE
FROM secondary menu (Chapter 18).
10-4 Matrices
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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.
Viewing-Context
Keys
Key
Function
| or ~
Moves the rectangular cursor within the
current row.
† or }
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 [INS]
Nothing
Nothing
{
Matrices 10-5
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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.
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.
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 [INS]
Activates the insert cursor.
{
Deletes the character under the edit cursor
on the bottom line.
10-6 Matrices
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Using Matrices with Expressions
Using a Matrix in To use a matrix in an expression, you can do any of the
an Expression
following.
•
•
Copy the name from the MATRX NAMES menu.
Recall the contents of the matrix into the expression
with y [RCL] (Chapter 1).
•
Enter the matrix directly (see below).
Entering a Matrix You can enter, edit, and store a matrix in the matrix editor.
in an Expression 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.
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.
Matrices 10-7
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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 Ž to display the MATRX NAMES menu.
2. Select the name of the matrix you want to copy.
3. Press ¿.
4. Press Ž 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
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.
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 (—
) to invert a matrix (^L1 is not
valid). matrix must be square. The determinant cannot
equal zero.
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
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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.
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)
Matrices 10-11
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Using the MATRX MATH Operations
MATRX MATH
Menu
To display the MATRX MATH menu, press Ž ~.
NAMES MATH EDIT
1:det(
2:
Calculates the determinant.
Transposes the matrix.
T
3:dim(
4:Fill(
Returns the matrix dimensions.
Fills all elements with a constant.
Returns the identity matrix.
Returns a random matrix.
Appends two matrices.
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.
5:identity(
6:randM(
7:augment(
8:Matr4list(
9:List4matr(
0:cumSum(
A:ref(
B:rref(
C:rowSwap(
D:row+(
E:ärow(
F:ärow+(
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 dim( (dimension) returns a list containing the dimensions
Dimensions with ({rows columns}) of matrix.
dim(
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 Use dim( with ¿ to create a new matrixname of
with dim(
dimensions rows × columns with 0 as each element.
{rows,columns}!dim(matrixname)
Redimensioning a Use dim( with ¿ to redimension an existing
Matrix with dim(
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.
Fill(value,matrixname)
identity(
randM(
identity( returns the identity matrix of dimension rows ×
dimension columns.
identity(dimension)
randM( (create random matrix) returns a rows × columns
L
random matrix of integers ‚ 9 and 9. The seed value
stored to the rand function controls the values (Chapter 2).
randM(rows,columns)
Matrices 10-13
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augment(
augment( appends matrixA to matrixB as new columns.
matrixA and matrixB both must have the same number of
rows.
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.
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)
&
10-14 Matrices
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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.
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.
rref(matrix)
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rowSwap(
rowSwap( returns a matrix. It swaps rowA and rowB of
matrix.
rowSwap(matrix,rowA,rowB)
row+(
row+( (row addition) returns a matrix. It adds rowA and
rowB of matrix and stores the results in rowB.
row+(matrix,rowA,rowB)
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)
10-16 Matrices
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Lists
11
Contents
Getting Started: Generating a Sequence.................. 11-2
Naming Lists............................................. 11-3
Storing and Displaying Lists ............................. 11-4
Entering List Names ..................................... 11-6
Attaching Formulas to List Names ....................... 11-7
Using Lists in Expressions ............................... 11-9
LIST OPS Menu.......................................... 11-10
LIST MATH Menu ........................................ 11-17
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Getting Started: Generating a Sequence
Getting Started is a fast-paced introduction. Read the chapter for details.
Calculate the first eight terms of the sequence 1/A2. 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 [LIST] ~ 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.
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 [LIST] to display the LIST NAMES
menu. Press Í to paste ÙSEQ1 to the
current cursor location. (If SEQ1 is not item
1 on your LIST NAMES menu, move the
cursor to SEQ1 before you press Í.)
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.
11-2 Lists
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Naming Lists
Using TI-83 List
Names L1
through L6
The TI-83 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 [ { ], enter one or more list elements, and then
press y [ } ]. 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.
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 memory
has space to store.
Lists 11-3
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Storing and Displaying Lists
Storing Elements You can store list elements in either of two ways.
to a List
•
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 To display the elements of a list on the home screen, enter
on the Home
Screen
the name of the list (preceded by Ù if necessary; see page
11.16), and then press Í. 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.
11-4 Lists
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Copying One List To copy a list, store it to another list.
to Another
Accessing a List You can store a value to or recall a value from a specific
Element
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 DELETE FROM secondary menu (Chapter 18).
Resetting memory restores L1 through L6. Removing a list
from the stat list editor does not delete it from memory.
Using Lists in
Graphing
You can use lists to graph a family of curves (Chapter 3).
Lists 11-5
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Entering List Names
Using the
LIST NAMES
Menu
To display the LIST NAMES menu, press y [LIST]. 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 (page 11.3).
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.
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 [LIST] ~ to display the LIST OPS menu.
2. Select B:Ù, which pastes Ù to the current cursor location.
Ù is not always necessary (page 11.16).
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.
11-6 Lists
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Attaching Formulas to List Names
Attaching a
You can attach a formula to a list name so that each list
Formula to a List element is a result of the formula. When executed, the
Name
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.
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).
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Attaching a
To attach a formula to a list name from a blank line on the
Formula to a List home screen or from a program, follow these steps.
on the Home
Screen or in a
Program
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 list name L1
through L6.
Press y [LIST] and select a user.created list name
from the LIST NAMES menu.
Enter a user.created list name directly using Ù (page
11.16).
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.
Detaching a
Formula from a
List
You can detach (clear) an attached formula from a list in
any of three ways.
•
•
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).
Note: You also can use ClrList or ClrAllList to detach a formula
from a list (Chapter 18).
11-8 Lists
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Using Lists in Expressions
Using a List in an You can use lists in an expression in any of three ways.
Expression
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 (step 1 on page 11.3).
Use y [RCL] 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.
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.
Lists 11-9
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LIST OPS Menu
LIST OPS Menu
To display the LIST OPS menu, press y [LIST] ~.
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(
5:seq(
Fills all elements with a constant.
Creates a sequence.
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).
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).
11-10 Lists
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Using dim( to
Find List
dim( (dimension) returns the length (number of elements)
of list.
Dimensions
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.
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).
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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.
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)
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 (page 11.13).
11-12 Lists
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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).
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 [LIST] ~ 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.
5. Press | and ~ to move the cursor to the stat plot data
point that you want as the left bound.
Lists 11-13
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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.
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.
11-14 Lists
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augment(
augment( concatenates the elements of listA and listB. The
list elements can be real or complex numbers.
augment(listA,listB)
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)
&
Lists 11-15
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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)
&
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 may misinterpret a user-created list name as implied
multiplication of two or more characters.
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 will ignore the entry.
11-16 Lists
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LIST MATH Menu
LIST MATH Menu To display the LIST MATH menu, press y [LIST] |.
NAMES OPS MATH
1:min(
2:max(
Returns minimum element of a list.
Returns maximum element of a list.
Returns mean of a list.
3:mean(
4:median(
5:sum(
6:prod(
7:stdDev(
8:variance(
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.
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.
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
You can combine sum( or prod( with seq( to obtain:
upper
expression(x)
upper
expression(x)
Sequences
∏
G
x=lower
x=lower
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])
11-18 Lists
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Statistics
12
Contents
Getting Started: Pendulum Lengths and Periods ......... 12-2
Setting Up Statistical Analyses........................... 12-10
Using the Stat List Editor ................................ 12-11
Attaching Formulas to List Names ....................... 12-14
Detaching Formulas from List Names.................... 12-16
Switching Stat List Editor Contexts ...................... 12-17
Stat List Editor Contexts................................. 12-18
STAT EDIT Menu ........................................ 12-20
Regression Model Features .............................. 12-22
STAT CALC Menu........................................ 12-24
Statistical Variables...................................... 12-29
Statistical Analysis in a Program ......................... 12-30
Statistical Plotting ....................................... 12-31
Statistical Plotting in a Program ......................... 12-37
Statistics 12-1
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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)
6.5
Time (sec)
0.51
11.0
0.68
13.2
0.73
15.0
0.79
18.0
0.88
23.1
0.99
24.4
1.01
26.6
1.08
30.5
1.13
34.3
1.26
37.6
1.28
41.5
1.32
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.
*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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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
on page 12.2.
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 on
page 12.2.
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 [STAT PLOT] 1 to select 1:Plot1
from the STAT PLOTS menu. The stat
plot editor is displayed for plot 1.
8. Press Í to select On, which turns on
plot 1. Press † Í to select "
(scatter plot). Press † y [L1] to
specify Xlist:L1 for plot 1. Press †
y [L2] 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.
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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.
11. Press y [L1] ¢ y [L2] ¢. 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.
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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.
14. Press … 1 to select 1:Edit. The stat
list editor is displayed.
Press ~ and } to move the cursor onto
L3.
Press y [INS]. 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 [LIST] 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.
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.
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18. Press y [STAT PLOT] 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 [L1] 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.
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.
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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.
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 [L1] ¢ y [L2] ¢. 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.
26. Press s. The regression line and the
scatter plot are displayed.
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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.
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.
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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.
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.
32. Press y [ENTRY] 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 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.
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 (page 12.17).
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 [INS]. 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.
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 (page 12.12).
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 To create a name in the stat list editor, follow these steps.
in the Stat List
Editor
1. Follow step 1 on page 12.11 to display the Name=
prompt.
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
To remove a list from the stat list editor, move the cursor
from the Stat List onto the list name and then press {. The list is not deleted
Editor
from memory; it is only removed from the stat list editor.
Note: To delete a list name from memory, use the MEMORY
DELETE:List selection screen (Chapter 18).
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.
•
•
Use SetUpEditor with no arguments (page 12.21).
Reset all memory (Chapter 18).
Clearing All
Elements from a
List
You can clear all elements from a list in any of five ways.
•
•
Use ClrList to clear specified lists (page 12.20).
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 [INS], 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.
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
You can attach a formula to a list name in the stat list
Formula to a List editor, and then display and edit the calculated list
Name in Stat List elements. When executed, the attached formula must
Editor
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.
4. Press ƒ [ã], enter the formula, and press ƒ [ã].
Note: If you do not use quotation marks, the TI-83 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 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
When you edit an element of a list referenced in an
List Editor When attached formula, the TI-83 updates the corresponding
Formula-
Generated Lists
Are Displayed
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 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.
Handling Errors
Resulting from
Attached
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.
Formulas
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 any of
four ways.
•
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.
•
•
Use ClrList (page 12.20). All elements of one or more
specified lists are cleared, 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.
Editing an
Element of a
Formula-
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 protects against
inadvertently detaching the formula from the list name by
editing an element of the formula-generated list.
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
View-names context
•
•
Edit-elements 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.
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 [INS]. 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 [INS]. 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.
•
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 [INS].
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.
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...
2:SortA(
3:SortD(
4:ClrList
5:SetUpEditor
Displays the stat list editor.
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.
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.
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.
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.
Restoring L1
SetUpEditor with no listnames removes all list names from
through L6 to the the stat list editor and restores list names L1 through L6 in
Stat List Editor
the stat list editor columns 1 through 6.
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Regression Model Features
Regression
Model Features
STAT CALC menu items 3 through C are regression models
(page 12.24). 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 uses the formula below to compute RESID list
elements. The next section describes the variable RegEQ.
RESID = Ylistname N RegEQ(Xlistname)
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
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
computes and stores diagnostics values for r (correlation
2
2
coefficient) and r (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
2
example, for ExpReg (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).
Note: To set DiagnosticOn or DiagnosticOff from the home
screen, press y [CATALOG], 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
4:LinReg(ax+b)
5:QuadReg
6:CubicReg
7:QuartReg
8:LinReg(a+bx)
9:LnReg
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.
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.
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 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.
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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.
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]
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); when DiagnosticOn is set, it
2
also displays values for r and r.
LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]
QuadReg
QuadReg (quadratic regression) fits the second-degree
polynomial y=ax2+bx+c to the data. It displays values for a,
b, and c; when DiagnosticOn is set, it also displays a value
(ax2+bx+c)
2
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]
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CubicReg
CubicReg (cubic regression) fits the third-degree
(ax3+bx2+cx+d)
polynomial y=ax3+bx2+cx+d to the data. It displays values
for a, b, c, and d; when DiagnosticOn is set, it also displays
2
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.
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; when DiagnosticOn is set, it also
2
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); when DiagnosticOn is set, it
2
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
2
b; when DiagnosticOn is set, it also displays values for r
and r.
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
2
DiagnosticOn is set, it also displays values for r and r.
ExpReg [Xlistname,Ylistname,freqlist,regequ]
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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
2
DiagnosticOn is set, it also displays values for r and r.
PwrReg [Xlistname,Ylistname,freqlist,regequ]
Logistic
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.
c/(1+aäeLbx
)
Logistic [Xlistname,Ylistname,freqlist,regequ]
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.
A SinReg example is shown on the next page.
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SinReg Example: Compute the regression model for the number of hours of
Daylight Hours in daylight in Alaska during one year.
Alaska for 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.
•
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.
Variables
1.Var
2.Var
Other
VARS
Stats
Stats
menu
mean of x values
v
v
XY
G
sum of x values
Gx
Gx
2
2
2
sum of x values
Gx
Gx
G
sample standard deviation of x
population standard deviation of x
number of data points
mean of y values
Sx
sx
n
Sx
sx
XY
XY
XY
XY
G
n
w
sum of y values
Gy
2
sum of y values
Gy2
G
sample standard deviation of y
population standard deviation of y
sum of x … y
Sy
XY
XY
G
sy
Gxy
minX
maxX
minY
maxY
minimum of x values
maximum of x values
minimum of y values
maximum of y values
1st quartile
minX
maxX
XY
XY
XY
XY
PTS
PTS
PTS
EQ
EQ
Q1
Med
Q3
median
3rd quartile
regression/fit coefficients
a, b
polynomial, Logistic, and SinReg
coefficients
a, b, c,
d, e
correlation coefficient
r
EQ
EQ
2
2
coefficient of determination
regression equation
r , R
RegEQ
EQ
summary points (Med.Med only)
x1, y1, x2,
y2, x3, y3
PTS
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 You can plot statistical data that is stored in lists. The six
Statistical Data in types of plots available are scatter plot, xyLine, histogram,
Lists
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.
"
(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 SortA( or SortD( to sort the lists
before you plot them (page 12.20).
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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.
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 (page 12.29).
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.
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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 (page 12.29).
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 plots the data on the x-axis and
the z-values on the y-axis.
If you select Y, the TI-83 plots the data on the y-axis and
the z-values on the x-axis.
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Defining the
Plots
To define a plot, follow these steps.
1. Press y [STAT PLOT]. The STAT PLOTS menu is
displayed with the current plot definitions.
2. Select the plot you want to use. The stat plot editor is
displayed for the plot you selected.
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 Data
List Axis
XList YList Mark Freq
"
Scatter
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Ó xyLine
Ò Histogram
Õ ModBoxplot
Ö Boxplot
Ô NormProbPlot
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 ¦)
Freq (frequency list for Xlist elements; default is 1)
Data List (list name for NormProbPlot)
Data Axis (axis on which to plot Data List)
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Displaying Other Each stat plot has a unique stat plot editor. The name of
Stat Plot Editors
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.
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).
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Defining the
Stat plots are displayed on the current graph. To define the
Viewing Window 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.
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
To display a stat plot from a program, define the plot, and
Plot in a Program 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 [STAT PLOT] to display the STAT PLOTS menu.
2. Select the plot to define, which pastes Plot1(, Plot2(, or
Plot3( to the cursor location.
3. Press y [STAT PLOT] ~ to display the STAT TYPE
menu.
4. Select the type of plot, which pastes the name of the
plot type to the cursor location.
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5. Press ¢. Enter the list names, separated by commas.
6. Press ¢ y [STAT PLOT] | 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.
7. Press ¤ Í to complete the command line.
Displaying a Stat To display a plot from a program, use the DispGraph
Plot from a
Program
instruction (Chapter 16) or any of the ZOOM instructions
(Chapter 3).
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Inferential Statistics
and Distributions
13
Contents
Getting Started: Mean Height of a Population ............ 13-2
Inferential Stat Editors................................... 13-6
STAT TESTS Menu ...................................... 13-9
Inferential Statistics Input Descriptions.................. 13-26
Test and Interval Output Variables....................... 13-28
Distribution Functions................................... 13-29
Distribution Shading..................................... 13-35
Inferential Statistics and Distributions 13-1
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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 cm. and a standard deviation of 6.35 cm.
(randNorm(165.1,6.35,90) with a seed of 789).
Height (in cm.) 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
1. Press … Í to display the stat list
editor.
Press } to move the cursor onto L1, and
then press y [INS]. 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.
Enter the other nine height values the
same way.
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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.
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 cm. and 173.94 cm. This is about
a 14.2 cm. 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 cm. (introduction; page
13.2), 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.
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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
(introduction; page 13.2). 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.
8. Press † 163 Ë 8 Í to store 163.8 to þ.
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 cm. and a standard deviation σ of 6.35 cm., what height
is exceeded by only 5 percent of the women (the 95th percentile)?
10. Press ‘ to clear the home screen.
Press y [DISTR] 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 cm.
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 [DISTR] ~ to display the DISTR
DRAW menu.
14. Press Í to paste ShadeNorm( to the
home screen.
Press y [ANS] ¢ 1 y [EE] 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.
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.
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Select Data or
Stats input
Select an alternative
hypothesis
Enter values for
arguments
Select Calculate
or Draw output
Selecting Data or Most inferential stat editors prompt you to select one of
Stats
two types of input. (1.PropZInt and 2.PropZTest, 1.PropZInt
and 2.PropZInt, c2.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 know what a particular argument symbol
represents, see the tables on pages 13.26 and 13.27.
When you enter values in any inferential stat editor, the
TI.83 stores them in memory so that you can run many
tests or intervals without having to reenter every value.
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.
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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.
Selecting
After you have entered all arguments in an inferential stat
Calculate or Draw editor for a hypothesis test, you must select whether you
for a Hypothesis want to see the calculated results on the home screen
Test
(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
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.
Calculate for a
Confidence
Interval
When you press Í, Calculate calculates the confidence
interval results and displays the outputs on the home
screen.
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. Most of these output variables are in the TEST
secondary menu (VARS menu; 5:Statistics). For a list of
these variables, see page 13.28.
EDIT CALC TESTS
1:Z-Test...
2:T-Test...
Test for 1 m, known s
Test for 1 m, unknown s
3:2-SampZTest... Test comparing 2 m’s, known s’s
4:2-SampTTest... Test comparing 2 m’s, unknown s’s
5:1-PropZTest... Test for 1 proportion
6:2-PropZTest... Test comparing 2 proportions
7:ZInterval... Confidence interval for 1 m, known s
8:TInterval... Confidence interval for 1 m, unknown s
9:2-SampZInt... Conf. int. for diff. of 2 m’s, known s’s
0:2-SampTInt... Conf. int. for diff. of 2 m’s, unknown s’s
A:1-PropZInt... Confidence int. for 1 proportion
B:2-PropZInt... Confidence int. for diff. of 2 props
C:c2-Test...
Chi-square test for 2-way tables
D:2-SampÛTest... Test comparing 2 s’s
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:
,
,
Calculated results:
,
,
Drawn results:
Note: All examples on pages13.10 through 13.25 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.
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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)
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:
,
,
Calculated results:
,
,
Drawn results:
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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)
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:
,
,
Drawn results:
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)
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:
,
,
Calculated results:
Drawn results:
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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 (x1 and x2) and the count of observations in
each sample (n1 and n2). 2.PropZTest tests the null
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)
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:
,
,
Calculated results:
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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}
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
(x1 and x2) and the count of observations in each sample
(n1 and n2). The computed confidence interval depends on
the user-specified confidence level.
Input:
,
Calculated results:
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2
c2-Test
c .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 Ž ~ ~ 1 to
select 1:[A] from the MATRX
EDIT menu.
Matrix editor:
Input:
Note: Press Ž [B] Í to
display matrix [B].
,
Calculated results:
,
Drawn results:
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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={
7
L4 18 17 L3 L5 1 10 11 L2}
SAMP5={ L1 12 L1 L3
3
L5
5
2 L11 L1 L3}
Data
Stats
Input:
,
,
,
,
Calculated results:
Drawn results:
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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)
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={38 56 59 64 74}
L4={41 63 70 72 84}
Input:
,
Calculated results:
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.
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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}
Input:
,
Calculated results:
Note: SS is sum of squares and MS is mean square.
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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
m0
Hypothesized value of the population mean that you are
testing.
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.
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
Freq1, Freq2
The names of the lists containing the data you are testing
for the two-sample tests and intervals. Defaults are L1 and
L2, respectively.
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, n2
Summary statistics (mean, standard deviation, and 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.
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Input
p0
Description
The expected sample proportion for 1.PropZTest. Must be a
real number, such that 0 < p0 < 1.
x
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.
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
c2.Test. Observed must contain all integers ‚ 0. Matrix
dimensions must be at least 2×2.
Expected (Matrix) The matrix name that specifies where the expected values
should be stored. Expected is created upon successful
completion of the c2.Test.
Xlist, Ylist
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.
Inferential Statistics and Distributions 13-27
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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, VARS
Variables
Tests
p
Intervals ANOVA
Menu
TEST
TEST
TEST
TEST
p-value
p
2
test statistics
degrees of freedom
z, t, c , 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,
TEST
TEST
Sx2
number of data points for sample n1, n2
1 and sample 2
n1, n2
pooled standard deviation
SxP
SxP
Ç
SxP
TEST
TEST
TEST
estimated sample proportion
Ç
estimated sample proportion for Ç1
population 1
Ç1
estimated sample proportion for Ç2
Ç2
TEST
TEST
population 2
confidence interval pair
lower,
upper
mean of x values
v
v
XY
sample standard deviation of x
number of data points
standard error about the line
regression/fit coefficients
correlation coefficient
coefficient of determination
regression equation
Sx
n
Sx
n
XY
XY
s
TEST
EQ
EQ
EQ
EQ
a, b
r
2
r
RegEQ
13-28 Inferential Statistics and Distributions
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Distribution Functions
DISTR menu
To display the DISTR menu, press y [DISTR].
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(
6:c2pdf(
7:c2cdf
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.
normalpdf(
norwmalpdf( 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
−
e
1
2σ2
f(x) =
, σ >0
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.
Inferential Statistics and Distributions 13-29
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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])
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
13-30 Inferential Statistics and Distributions
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tcdf(
tcdf( computes the Student-t distribution probability
between lowerbound and upperbound for the specified df
(degrees of freedom), which must be > 0.
tcdf(lowerbound,upperbound,df)
c2pdf(
c2pdf( computes the probability density function (pdf) for
the c2 (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
x
df /2 −1 e − x/2 , x ≥0
Γ (df /2)
c2pdf(x,df)
Note: For this example,
Xmin = 0
Xmax = 30
Ymin = L.02
Ymax = .132
2
2
c2cdf(
c cdf( computes the c (chi-square) distribution probability
between lowerbound and upperbound for the specified df
(degrees of freedom), which must be an integer > 0.
2
c cdf(lowerbound,upperbound,df)
Inferential Statistics and Distributions 13-31
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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:
n/ 2
Γ [(n + d)/2]
Γ (n/2)Γ (d/2)
n
d
f(x) =
xn/2 −1 (1+nx/d) −(n +d)/2 , x ≥0
where
n = numerator degrees of freedom
d = denominator degrees of freedom
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)
13-32 Inferential Statistics and Distributions
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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 probabilities
from 0 to numtrials is returned. The probability density
function (pdf) is:
n
f(x) =
px(1− p)n − x , x =0,1,ꢀ,n
x
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])
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 −µµx /x! , x =0,1,2,ꢀ
poissonpdf(m,x)
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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)
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)
13-34 Inferential Statistics and Distributions
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Distribution Shading
DISTR DRAW
Menu
To display the DISTR DRAW menu, press y [DISTR] ~.
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( Shades normal distribution.
2:Shade_t(
3:Shadec2(
4:ShadeÛ(
Shades Student-t distribution.
Shades c2 distribution.
Shades Û distribution.
Note: L1å99 and 1å99 specify infinity. If you want to view the area left
of upperbound, for example, specify lowerbound=L1å99.
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
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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.
Shade_t(lowerbound,upperbound,df)
Note: For this example,
Xmin = L3
Xmax = 3
Ymin = L.15
Ymax = .5
2
2
Shadec2(
Shadec ( draws the density function for the c (chi-square)
distribution specified by df (degrees of freedom) and shades
the area between lowerbound and upperbound.
2
Shadec (lowerbound,upperbound,df)
Note: For this example,
Xmin = 0
Xmax = 35
Ymin = L.025
Ymax = .1
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
13-36 Inferential Statistics and Distributions
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Financial
Functions
14
Contents
Getting Started: Financing a Car ......................... 14-2
Getting Started: Computing Compound Interest.......... 14-3
Using the TVM Solver .................................... 14-4
Using the Financial Functions ........................... 14-5
Calculating Time Value of Money (TVM) ................. 14-6
Calculating Cash Flows .................................. 14-8
Calculating Amortization ................................ 14-9
Calculating Interest Conversion.......................... 14-12
Finding Days between Dates/Defining Payment Method ..... 14-13
Using the TVM Variables ................................. 14-14
Financial Functions 14-1
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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
will display all numbers with two decimal
places.
2. Press y [FINANCE] to display the
FINANCE CALC menu.
3. Press Í to select 1:TVM Solver. 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. 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 [SOLVE] to
solve for æ. What APR should you look
for?
14-2 Financial Functions
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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 y [FINANCE] to display the
FINANCE CALC menu.
2. Press Í to select 1:TVM Solver. 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.
3. Press } } } } } to place the cursor on
the æ prompt.
4. Press ƒ [SOLVE] to solve for æ, the
annual interest rate.
Financial Functions 14-3
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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.
The FINANCE VARS menu section (page 14.14) describes
the five TVM variables (Ú, æ, 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 y [FINANCE] Í to display the TVM Solver. The
screen below shows the default values with the fixed-
decimal mode set to two decimal places.
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 [SOLVE]. 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.
14-4 Financial Functions
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Using the Financial Functions
Entering Cash
When using the TI-83 financial functions, you must enter
Inflows and Cash cash inflows (cash received) as positive numbers and cash
Outflows
outflows (cash paid) as negative numbers. The TI-83
follows this convention when computing and displaying
answers.
FINANCE CALC
Menu
To display the FINANCE CALC menu, press y [FINANCE].
CALC VARS
1:TVM Solver... Displays the TVM Solver.
2:tvm_Pmt
3:tvm_æ
4:tvm_PV
5:tvm_Ú
6:tvm_FV
7:npv(
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.
8:irr(
9:bal(
Computes the internal rate of return.
Computes the amortization sched. balance.
Computes the amort. sched. principal sum.
Computes the amort. sched. interest sum.
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).
0:GPrn(
A:GInt(
B:4Nom(
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
TVM Solver displays the TVM Solver (page 14.4).
Financial Functions 14-5
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Calculating Time Value of Money (TVM)
Calculating Time Use time-value-of-money (TVM) functions (menu items 2
Value of Money
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 are not stored to the TVM
variables (page 14.14).
Note: To store a value to a TVM variable, use the TVM Solver (page
14.4) or use ¿ and any TVM variable on the FINANCE VARS
menu (page 14.14).
If you enter less than six arguments, the TI-83 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.
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.
14-6 Financial Functions
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tvm_æ
tvm_æ computes the annual interest rate.
tvm_æ[(Ú,PV,PMT,FV,P/Y,C/Y)]
tvm_PV
tvm_PV computes the present value.
tvm_PV[(Ú,æ,PMT,FV,P/Y,C/Y)]
tvm_Ú
tvm_Ú computes the number of payment periods.
tvm_Ú[(æ,PV,PMT,FV,P/Y,C/Y)]
tvm_FV
tvm_FV computes the future value.
tvm_FV[(Ú,æ,PV,PMT,P/Y,C/Y)]
Financial Functions 14-7
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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
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
14-8 Financial Functions
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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 uses the current Float/Fix decimal-mode
setting.
bal(npmt[,roundvalue])
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 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 uses
the current Float/Fix decimal-mode setting.
GInt(pmt1,pmt2[,roundvalue])
Financial Functions 14-9
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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 y [FINANCE] Í to display the TVM Solver.
3. Press 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.
4. Press } } } } } to place the cursor on the PV prompt.
Press ƒ [SOLVE] 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 † y
[FINANCE] 9 „¤ to define Y1T as bal(T).
14-10 Financial Functions
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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 [TBLSET] and enter the values below.
TblStart=0
@Tbl=12
9. Press y [TABLE] 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.
Financial Functions 14-11
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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)
14-12 Financial Functions
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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.
Defining the
Pmt_End and Pmt_Bgn (menu items E and F) specify a
Payment Method 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.
Financial Functions 14-13
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Using the TVM Variables
FINANCE VARS
Menu
To display the FINANCE VARS menu, press y [FINANCE]
~. You can use TVM variables in TVM functions and store
values to them on the home screen.
CALC VARS
1:Ú
2:æ
Total number of payment periods
Annual interest rate
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.
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.
14-14 Financial Functions
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CATALOG, Strings,
Hyperbolic Functions
15
Contents
Browsing the TI-83 CATALOG ........................... 15-2
Entering and Using Strings............................... 15-3
Storing Strings to String Variables ....................... 15-4
String Functions and Instructions in the CATALOG ...... 15-6
Hyperbolic Functions in the CATALOG .................. 15-10
CATALOG, Strings, Hyperbolic Functions 15-1
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Browsing the TI-83 CATALOG
What Is the
CATALOG?
The CATALOG is an alphabetical list of all functions and
instructions on the TI-83. You also can access each
CATALOG item from a menu or the keyboard, except:
•
•
•
The six string functions (page 15.6)
The six hyperbolic functions (page 15.10)
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(.
Selecting an Item To select a CATALOG item, follow these steps.
from the
CATALOG
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].
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.
15-2 CATALOG, Strings, Hyperbolic Functions
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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, 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 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.
•
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
[A.LOCK] 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.
CATALOG, Strings, Hyperbolic Functions 15-3
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Storing Strings to String Variables
String Variables
The TI-83 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.
15-4 CATALOG, Strings, Hyperbolic Functions
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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.
Displaying the
Contents of a
String Variable
To display the contents of a string variable on the home
screen, select the string variable from the VARS STRING
menu, and then press Í. The string is displayed.
CATALOG, Strings, Hyperbolic Functions 15-5
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String Functions and Instructions in the CATALOG
Displaying String String functions and instructions are available only from
Functions and
Instructions in
the CATALOG
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( Converts an equation to a string.
expr(
...
inString(
...
length(
...
Converts a string to an expression.
Returns a character’s place number.
Returns a string’s character length.
String4Equ( Converts a string to an equation.
sub(
Returns a string subset as a string.
...
+ (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 To select a string function or instruction and paste it to the
Function from
the CATALOG
current screen, follow the steps on page 15.2.
15-6 CATALOG, Strings, Hyperbolic Functions
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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)
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.
CATALOG, Strings, Hyperbolic Functions 15-7
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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)
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)
15-8 CATALOG, Strings, Hyperbolic Functions
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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)
Entering a
Function to
Graph during
Program
In a program, you can enter a function to graph during
program execution using these commands.
Execution
Note: When you execute this program, enter a function to store to Y3
at the ENTRY= prompt.
CATALOG, Strings, Hyperbolic Functions 15-9
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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(
cosh
...
Hyperbolic cosine
Hyperbolic arccosine
L1
(
(
(
sinh(
Hyperbolic sine
Hyperbolic arcsine
L1
sinh
...
tanh(
Hyperbolic tangent
Hyperbolic arctangent
L1
tanh
...
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)
L1
L1
sinhL1(, coshL1(,
tanhL1(
sinh ( is the hyperbolic arcsine function. cosh ( is the
L1
hyperbolic 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)
15-10 CATALOG, Strings, Hyperbolic Functions
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16
Contents
Getting Started: Volume of a Cylinder.................... 16-2
Creating and Deleting Programs ......................... 16-4
Entering Command Lines and Executing Programs ...... 16-5
Editing Programs ........................................ 16-6
Copying and Renaming Programs........................ 16-7
PRGM CTL (Control) Instructions ....................... 16-8
PRGM I/O (Input/Output) Instructions ................... 16-16
Calling Other Programs as Subroutines .................. 16-22
Programming 16-1
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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 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.
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
2
pR H and store it to the variable V.
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5. Press ~ 3 to select 3:Disp from the
PRGM I/O menu. Disp is pasted to the
command line. Press y [A.LOCK] 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 [QUIT] to display the home
screen.
7. Press to display the PRGM EXEC
menu. The items on this menu are the
names of stored programs.
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.
Programming 16-3
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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 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 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.
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 (page 16.5).
7. Press y [QUIT] 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, press y [MEM], and then
select 1:Check RAM from the MEMORY menu (Chapter 18).
To increase available memory, press y [MEM], and then
select 2:Delete from the MEMORY menu (Chapter 18).
To delete a specific program, press y [MEM], select
2:Delete from the MEMORY menu, and then select 7:Prgm
from the DELETE FROM secondary menu (Chapter 18).
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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 (page 16.15
and page 16.22).
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
(page 16.7). 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 checks for errors during program execution. It
does not check for errors as you enter a program.
Breaking a
Program
To stop program execution, press É. The ERR:BREAK
menu is displayed.
•
•
To return to the home screen, select 1:Quit.
To go where the interruption occurred, select 2:Goto.
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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 (page
16.7). 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 }.
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
[INS], 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.
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Copying and Renaming Programs
Copying and
Renaming a
Program
To copy all command lines from one program into a new
program, follow steps 1 through 5 for Creating a New
Program (page 16.4), and then follow these steps.
1. Press y [RCL]. 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.
Note: You also can copy all the command lines from one existing
program to another existing program using RCL.
Scrolling the
The TI-83 sorts PRGM EXEC and PRGM EDIT menu items
PRGM EXEC and automatically into alphanumerical order. Each menu only
PRGM EDIT
Menus
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 }.
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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
3:Else
4:For(
5:While
6:Repeat
7:End
8:Pause
9:Lbl
Executes commands when If is true.
Executes commands when If is false.
Creates an incrementing loop.
Creates a conditional loop.
Creates a conditional loop.
Signifies the end of a block.
Pauses program execution.
Defines a label.
0:Goto
Goes to a label.
A:IS>(
B:DS<(
C:Menu(
D:prgm
E:Return
F:Stop
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.
Stops execution.
G:DelVar
H:GraphStyle(
Deletes a variable from within program.
Designates the graph style to be drawn.
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 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
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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.
:If condition
:command (if true)
:command
Program
Output
If.Then
Then following an If executes a group of commands if
condition is true (nonzero). End identifies the end of the
group of commands.
:If condition
:Then
:command (if true)
:command (if true)
:End
:command
Program
Output
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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
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
Program
Output
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While
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
Program
Output
Repeat
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
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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]
Program
Output
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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
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.
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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.
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.
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prgm
Use prgm to execute other programs as subroutines (page
16.22). 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
Note: You cannot directly enter the subroutine name when using RCL.
You must paste the name from the PRGM EXEC menu (page 16.7).
Return
Return quits the subroutine and returns execution to the
calling program (page 16.22), 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
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)
5 = ë (path)
6 = ì (animate)
3 = é (shade above) 7 = í (dot)
4 = ê (shade below)
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.
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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
2:Prompt
3:Disp
Enters a value or uses the cursor.
Prompts for entry of variable values.
Displays text, value, or the home screen.
Displays the current graph.
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.
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 ‘.
Displaying a
Input without a variable displays the current graph. You
Graph with Input can move the free-moving cursor, which updates X and Y
(and R and q for PolarGC format). The pause indicator is
on. Press Í to resume program execution.
Input
Program
Output
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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
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.
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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
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 (page 16.12).
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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
Output(
DispTable (display table) displays the current table. The
program halts temporarily so you can examine the screen.
Press Í to resume execution.
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 (page 16.20).
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)
Program
Output
For Output( on a Horiz split screen, the maximum value for
row is 4.
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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: , Ž, , and
Í were pressed during
program execution.
Note: You can press É at any time during execution to break the
program (page 16.5).
TI-83 Key Code
Diagram
ClrHome,
ClrTable
ClrHome (clear home screen) clears the home screen
during program execution.
ClrTable (clear table) clears the values in the table during
program execution.
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GetCalc(
GetCalc( gets the contents of variable on another TI-83 and
stores it to variable on the receiving TI-83. 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.82s and TI-83s.
Get(, Send(
Get( gets data from the Calculator-Based Laboratoryé
(CBL 2é, CBLé) System or Calculator-Based Rangeré
(CBRé) and stores it to variable on the receiving TI-83.
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 from a TI.82, the TI-83 will interpret it as the Get( described
above. Use GetCalc( to get data from another TI-83.
Send( sends the contents of variable to the CBL 2/CBL or
CBR. You cannot use it to send to another TI-83. 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.
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).
Programming 16-21
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Calling Other Programs as Subroutines
Calling a
Program from
On the TI-83, any stored program can be called from
another program as a subroutine. Enter the name of the
Another Program 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 (page 16.7). 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 (page 16.15).
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.
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.
16-22 Programming
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Applications
17
Contents
Comparing Test Results Using Box Plots ................ 17-2
Graphing Piecewise Functions........................... 17-4
Graphing Inequalities .................................... 17-5
Solving a System of Nonlinear Equations ................ 17-6
Using a Program to Create the Sierpinski Triangle ....... 17-7
Graphing Cobweb Attractors ............................ 17-8
Using a Program to Guess the Coefficients............... 17-9
Graphing the Unit Circle and Trigonometric Curves...... 17-10
Finding the Area between Curves ........................ 17-11
Using Parametric Equations: Ferris Wheel Problem...... 17-12
Demonstrating the Fundamental Theorem of Calculus... 17-14
Computing Areas of Regular N-Sided Polygons .......... 17-16
Computing and Graphing Mortgage Payments ........... 17-18
Applications 17-1
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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
4
1
7
8
12
6
12
11
10
8
12
7
8
7
5
7
8
11
4
10
14
13
5
12
12
7
11
12
8
12
11
9
12
11
11
13
12
11
12
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).
5. Press y [STAT PLOT]. 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.
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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.
%
%
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?
Applications 17-3
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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 … 10 + 10 (X N 55)
Y = 50 + 5 … 10 + 10 … 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).
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 [QUIT] 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?
17-4 Applications
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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.
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.
Applications 17-5
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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).
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 [CALC] 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.
17-6 Applications
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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:SIERPINS
:FnOff :ClrDraw
:PlotsOff
Program
:AxesOff
:0!Xmin:1!Xmax
Set viewing window.
:0!Ymin:1!Ymax
:rand!X:rand!Y
:For(K,1,3000)
Beginning of For group.
:rand!N
:If N1à3
:Then
:.5X!X
:.5Y!Y
If/Then group
:End
: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)
:End
:StorePic 6
Draw point.
End of For group.
Store picture.
After you execute the program above, you can recall and
display the picture with the instruction RecallPic 6.
Applications 17-7
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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 [FORMAT]. 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 [QUIT] 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
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.
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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:GUESS
:PlotsOff :Func
:FnOff :Radian
:ClrHome
Program
:"Asin(BX)"!Y1
:"Csin(DX)"!Y2
:GraphStyle(1,1)
:GraphStyle(2,5)
:FnOff 2
Define equations.
Set line and path graph
styles.
:randInt(1,10)!A
:randInt(1,10)!B
:0!C:0!D
:L2p!Xmin
:2p!Xmax
Initialize coefficients.
Set viewing window.
:pà2!Xscl
:L10!Ymin
:10!Ymax
:1!Yscl
:DispGraph
Display graph.
:Pause
:FnOn 2
:Lbl Z
:Prompt C,D
:DispGraph
Prompt for guess.
Display graph.
:Pause
:If C=A
:Text(1,1,"C IS OK")
:If CƒA
Display results.
:Text(1,1,"C IS WRONG")
:If D=B
: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.
Applications 17-9
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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
Xmin=L2
Xmax=7.4
Xscl=pà2
Ymin=L3
Ymax=3
Yscl=1
Tmax=2p
Tstep=.1
3. Press o. Turn off all functions and stat plots. Enter the
expressions to define the unit circle centered on (0,0).
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.
17-10 Applications
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Finding the Area between Curves
Problem
Find the area of the region bounded by
f(x)
g(x)
x
= 300x / (x2 + 625)
= 3cos(.1x)
= 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)
4. Press y [CALC] 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 [QUIT] to go to the home screen. Press
y [DRAW] 7 and use Shade( to see the area graphically.
Shade(Y2,Y1,Ans,75)
6. Press y [QUIT] 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.
Applications 17-11
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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
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
Xmin=L13
Xmax=34
Xscl=10
Ymin=0
Ymax=31
Yscl=10
Tmax=12
Tstep=.1
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.
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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
Xmin=0
Ymin=10
Ymax=25.5
Yscl=10
Tmax=3
Tstep=.03
Xmax=23.5
Xscl=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.
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.
Applications 17-13
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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:
F(x) = ‰ x 1àt dt = ln(x), x > 0 and that
1
D [‰ x 1àt dt]= 1àx
x
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
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.
17-14 Applications
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Problem 2
Explore the functions defined by
x
y = ‰ t2 dt, ‰ x t2 dt, and ‰ x t2 dt
M2
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.
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.
Applications 17-15
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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 interactive solver editor is
displayed, press } to display the equation editor.
2
2. Enter the formula as 0=ANNB sin(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 [SOLVE]. 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 [SOLVE].
6. Enter N=8. To find the distance B, move the cursor onto
B, and then press ƒ [SOLVE]. Find B for N=9, and
then for N=10.
17-16 Applications
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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 [SOLVE]. Find A for N=10, then
N=100, then N=150, then N=1000, and finally N=10000.
2
Notice that as N gets large, the area A approaches pB .
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.
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
2
2
p6 , which is approximately 113.097. Y2=pB (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.
Applications 17-17
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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 y [FINANCE] 1 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, 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 [SOLVE]. The present value, or mortgage amount,
of the house is displayed at the PV= prompt.
17-18 Applications
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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 CALC menu.
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.
Applications 17-19
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8. Press † to move the cursor onto the function for
interest defined by X2T and Y2T. Enter 240.
The graph shows that for the 240th payment (X=240),
441.97 of the 800 payment is interest (Y=441.97).
9. Press y [QUIT] y [FINANCE] 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?
17-20 Applications
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Management
18
Contents
Checking Available Memory ............................. 18-2
Deleting Items from Memory ............................ 18-3
Clearing Entries and List Elements ...................... 18-4
Resetting the TI-83 ...................................... 18-5
Memory Management 18-1
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Checking Available Memory
MEMORY Menu
To display the MEMORY menu, press y [MEM].
MEMORY
1:Check RAM...
2:Delete...
3:Clear Entries
4:ClrAllLists
5:Reset...
Reports memory availability/usage.
Displays DELETE FROM menu.
Clears ENTRY (last-entry storage).
Clears all lists in memory.
Displays RESET menu (all/defaults).
Displaying the
Check RAM
Screen
Check RAM displays the Check RAM screen. The top line
reports the total amount of available memory. The
remaining lines report the amount of memory each
variable type is using. You can check this screen to see
whether you need to delete variables from memory to
make room for new data, such as programs.
To check RAM usage, follow these steps.
1. Press y [MEM] to display the MEMORY menu.
2. Select 1:Check RAM to display the Check RAM screen.
The TI-83 expresses memory quantities in bytes.
Note: The $ in the left column of
the bottom row indicates that you
can scroll or page down to view
more variable types.
Note: Real, List, Y.Vars, and Prgm variable types never reset to
zero, even after memory is cleared.
To leave the Check RAM screen, press either y [QUIT] or
‘. Both options display the home screen.
18-2 Memory Management
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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, picture, graph database, or string),
follow these steps.
1. Press y [MEM] to display the MEMORY menu.
2. Select 2:Delete to display the DELETE FROM secondary
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 DELETE:List screen
is displayed.
4. Press } and † to move the selection cursor (4) next to
the item you want to delete, and then press Í. The
variable is deleted from memory. You can delete
individual variables one by one from this screen.
To leave any DELETE: screen without deleting anything,
press y [QUIT], which displays the home screen.
Note: You cannot delete some system variables, such as the last-
answer variable Ans and the statistical variable RegEQ.
Memory Management 18-3
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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 [MEM] 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.
ClrAllLists
ClrAllLists sets to 0 the dimension of each list in memory.
To clear all elements from all lists, follow these steps.
1. Press y [MEM] 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.
18-4 Memory Management
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Resetting the TI-83
RESET
The RESET secondary menu gives you the option of
Secondary Menu resetting all memory (including default settings) or
resetting the default settings while preserving other data
stored in memory, such as programs and Y= functions.
Resetting All
Memory
Resetting all memory on the TI-83 restores memory to the
factory settings. It deletes all nonsystem variables and all
programs. It resets all system variables to the default
settings.
Tip: Before you reset all memory, consider restoring sufficient
available memory by deleting only selected data (page 18.3).
To reset all memory on the TI-83, follow these steps.
1. Press y [MEM] to display the MEMORY menu.
2. Select 5:Reset to display the RESET secondary menu.
3. Select 1:All Memory to display the RESET MEMORY
tertiary menu.
4. Read the message below the RESET MEMORY menu.
•
•
To cancel memory reset and return to the home
screen, select 1:No.
To erase from memory all data and programs, select
2:Reset. All factory defaults are restored.
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 (Chapter 1).
Memory Management 18-5
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Resetting
Defaults
When you reset defaults on the TI-83, all defaults are
restored to the factory settings. Stored data and programs
are not changed.
These are some examples of TI-83 defaults that are
restored by resetting the defaults.
•
Mode settings such as Normal (notation); Func
(graphing); Real (numbers); and Full (screen)
•
•
Y= functions off
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
To reset all TI-83 factory defaults, follow these steps.
1. Press y [MEM] to display the MEMORY menu.
2. Select 5:Reset to display the RESET secondary menu.
3. Select 2:Defaults to display the RESET DEFAULTS
tertiary menu.
4. Consider the consequences of resetting defaults.
•
•
To cancel reset and return to the home screen, select
1:No.
To restore factory default settings, select 2:Reset.
Default settings are restored. Defaults set is
displayed on the home screen.
18-6 Memory Management
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Communication
Link
19
Contents
Getting Started: Sending Variables ....................... 19-2
TI-83 LINK ............................................... 19-3
Selecting Items to Send .................................. 19-4
Receiving Items.......................................... 19-5
Transmitting Items....................................... 19-6
Transmitting Lists to a TI-82 ............................. 19-8
Transmitting from a TI-82 to a TI-83 ..................... 19-9
Backing Up Memory ..................................... 19-10
Communication Link 19-1
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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.
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 [ [ ] y [ [ ] 1 ¢ 2 y [ ] ] y [ [
] 3 ¢ 4 y [ ] ] y [ ] ] ¿ Ž 1.
Press Í to store the matrix to [A].
3. Connect the calculators with the link
cable. Push both ends in firmly.
4. On the receiving unit, press y [LINK] ~ to
display the RECEIVE menu. Press 1 to
select 1:Receive. The message Waiting... is
displayed and the busy indicator is on.
5. On the sending unit, press y [LINK] to
display the SEND menu.
6. Press 2 to select 2:AllN. The AllN SELECT
screen is displayed.
7. Press † until the selection cursor ( 4 ) is
next to [A] MATRX. Press Í.
8. 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.
9. On the sending unit, press ~ to display the
TRANSMIT menu.
10. 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.
19-2 Communication Link
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TI-83 LINK
TI-83 Link
Capabilities
The TI-83 has a port to connect and communicate with
another TI-83, a TI-82, the Calculator-Based Laboratoryé
(CBL 2é, CBLé) System, the Calculator-Based Rangeré
(CBRé), or a personal computer. The unit-to-unit link
cable is included with the TI-83. This chapter describes
how to communicate with another calculator.
Linking Two
TI-83s
You can transfer all variables and programs to another
TI-83 or backup the entire memory of a TI-83. The
software that enables this communication is built into the
TI-83. To transmit from one TI-83 to another, follow the
steps on pages 19.6 and 19.7.
Linking a TI-82
and a TI-83
You can transfer from a TI-82 to a TI-83 all variables and
programs. Also, you can transfer from a TI-83 to a TI-82 lists
L1 through L6.
The software that enables this communication is built into the
TI-83. To transmit data from a TI-82 to a TI-83, follow the
steps on pages 19.6 and 19.7.
•
•
You cannot perform a memory backup from a TI-82 to a
TI-83.
The only data type you can transmit from a TI-83 to a
TI-82 is list data stored in L1 through L6. Use the LINK
SEND menu item 5:Lists to TI82 (page 19.8).
Connecting Two 1. Insert either end of the cable into the port very firmly.
Calculators with
the Cable
2. Insert the other end of the cable into the other
calculator’s port.
Linking to a CBR CBR and the CBL 2/CBL System are optional accessories
or the CBL 2/CBL that connect to a TI-83 with the unit-to-unit link cable.
System
With a CBR or a CBL 2/CBL and a TI-83, you can collect
and analyze real-world data.
Linking to a PC
or Macintosh
TI.GRAPH LINKé is an optional accessory that links a TI-83
to enable communication with a personal computer.
Communication Link 19-3
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Selecting Items to Send
LINK SEND Menu To display the LINK SEND menu, press y [LINK].
SEND RECEIVE
1:All+...
2:AllN...
3:Prgm...
4:List...
Displays all items selected.
Displays all items deselected.
Displays all programs names.
Displays all list names.
5:Lists to TI82...
6:GDB...
7:Pic...
8:Matrix...
9:Real...
0:Complex...
A:Y-Vars...
B:String...
C:Back Up...
Displays list names L1 through L6.
Displays all graph databases.
Displays all picture data types.
Displays all matrix data types.
Displays all real variables.
Displays all complex variables.
Displays all Y= variables.
Displays all string variables.
Selects all for backup to TI-83.
When you select an item on the LINK SEND menu, the
corresponding SELECT screen is displayed.
Note: Each SELECT screen, except All+ SELECT, is displayed
initially with no data selected.
Selecting Items
to Send
To select items to send on the sending unit, follow these
steps.
1. Press y [LINK] 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.
4. Press Í to select or deselect the item. Selected
names are marked with a 0.
5. Repeat steps 3 and 4 to select or deselect additional items.
19-4 Communication Link
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Receiving Items
LINK RECEIVE
Menu
To display the LINK RECEIVE menu, press y [LINK] ~.
SEND RECEIVE
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.
To transmit, follow the steps on page 19.6.
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 [QUIT] to exit the receive mode.
DuplicateName
Menu
During transmission, if a variable name is duplicated, the
DuplicateName menu is displayed on the receiving unit.
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.
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.
Communication Link 19-5
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Transmitting Items
Transmitting
Items
To transmit selected items after you have selected items to
send on the sending unit (page 19.4) and set the receiving
unit to receive (page 19.5), follow these steps.
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 (page 19.5).
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.
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.
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-82 and a TI-83.
You attempt a data transfer from a TI-83 to a TI-82 with
data other than lists L1 through L6 or without using
menu item 5:Lists to TI82.
•
•
•
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-82 instead of a TI-83.
19-6 Communication Link
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Transmitting
Items to an
Additional TI-83
After sending or receiving data, you can repeat the same
transmission to additional TI-83 units—from either the
sending unit or the receiving unit—without having to
reselect data to send. The current items remain selected.
Note: You cannot repeat transmission if you selected All+ or All..
To transmit to an additional TI-83, follow these steps.
1. Set the TI-83 to receive (page 19.5).
2. Do not select or deselect any new items to send. If you
select or deselect an item, all selections or deselections
from the previous transmission are cleared.
3. Disconnect the link cable from one TI-83 and connect it
to the additional TI-83.
4. Set the additional TI-83 to receive (page 19.5).
5. Press y [LINK] on the sending TI-83 to display the
LINK SEND menu.
6. Select the menu item that you used for the last
transmission. The data from your last transmission is
still selected.
7. Press ~ to display the LINK TRANSMIT menu.
8. Confirm that the receiving unit is set to receive
(page 19.5).
9. Press Í to select 1:Transmit and begin transmitting.
Communication Link 19-7
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Transmitting Lists to a TI-82
Transmitting
Lists to a TI-82
The only data type you can transmit from a TI-83 to a TI-82
is list data stored in L1 through L6.
To transmit to a TI-82 the list data that is stored to TI-83
lists L1, L2, L3, L4, L5, or L6, follow these steps.
1. Set the TI-82 to receive (page 19.5).
2. Press y [LINK] 5 on the sending TI-83 to select
5:Lists to TI82. The SELECT screen is displayed.
3. Select each list to transmit.
4. Press ~ to display the LINK TRANSMIT menu.
5. Confirm that the receiving unit is set to receive
(page 19.5).
6. Press Í to select 1:Transmit and begin transmitting.
Note: If dimension > 99 for a TI-83 list that is selected to send, the
receiving TI-82 will truncate the list at the ninety-ninth element during
transmission.
19-8 Communication Link
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Transmitting from a TI-82 to a TI-83
Resolved
Differences
Generally, you can transmit items to a TI-83 from a TI-82,
but differences between the two products may affect some
between the TI-82 transmitted data. This table shows differences for which
and TI-83
the software built into the TI-83 automatically adjusts
when a TI-83 receives TI-82 data.
TI.82
TI.83
nMin
nStart
Un
PlotStart
nMin
u
Vn
v
UnStart
VnStart
TblMin
u(nMin)
v(nMin)
TblStart
For example, if you transmit from a TI-82 to a TI-83 a
program that contains nStart on a command line and then
display the program on the receiving TI-83, you will see
that nMin has automatically replaced nStart on the
command line.
Unresolved
Differences
The software built into the TI-83 cannot resolve some
differences between the TI-82 and TI-83, which are
between the TI-82 described below. You must edit the data on the TI-83 after
and TI-83
you transmit to account for these differences, or the TI-83
will misinterpret the data.
The TI-83 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, the TI-83 reinterprets it as sin(X+5. Without a closing
parenthesis after X, the TI-83 interprets this as sin(X+5), not
the sum of 5 and sin(X).
If a TI-82 instruction that the TI-83 cannot translate is
transmitted, the ERR:INVALID menu is displayed when the
TI-83 attempts to execute the instruction. 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 cannot
directly translate Un-1 to the TI-83 syntax u(nN1), so the
ERR:INVALID menu is displayed.
Note: TI-83 implied multiplication rules differ from those of the TI.82.
For example, the TI-83 evaluates 1à2X as (1à2)äX, while the TI-82
evaluates 1à2X as 1à(2äX) (Chapter 2).
Communication Link 19-9
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Backing Up Memory
Memory Backup
To copy the exact contents of memory in the sending TI-83
to the memory of the receiving TI-83, put the other unit in
receive mode. Then, on the receiving unit, select C:Back Up
from the LINK SEND menu.
•
Warning: C:Back Up overwrites the memory in the
receiving unit; all information in the memory of the
receiving unit is lost.
Note: If you do not want to do a backup, select 2:Quit to return to
the LINK SEND menu.
•
Select 1:Transmit to begin transmission.
Receiving Unit
As a safety check to prevent accidental loss of memory,
the message WARNING . Backup is displayed when the
receiving unit receives notice of a backup.
•
To continue with the backup process, select 1:Continue.
The backup transmission begins.
•
To prevent the backup, select 2:Quit.
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.
19-10 Communication Link
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Tables and Reference
Information
A
Contents
Table of Functions and Instructions ..................... A-2
TI.83 Menu Map ......................................... A-39
Variables ................................................ A-49
Statistics Formulas ...................................... A-50
Financial Formulas ...................................... A-54
Tables and Reference Information A-1
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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 keystrokes that are valid in the program editor only. 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.
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(
2-13
10-10
abs(complex value)
Returns the magnitude of a
complex number or list.
CPX
5:abs(
2-19
valueA and valueB
Returns 1 if both valueA and
valueB are ƒ 0. valueA and
valueB can be real numbers,
expressions, or lists.
y [TEST]
LOGIC
1:and
2-26
angle(value)
Returns the polar angle of a
complex number or list of
complex numbers.
CPX
4:angle(
2-19
ANOVA(list1,list2
[,list3,...,list20])
Performs a one-way analysis of …
variance for comparing the
means of two to 20
populations.
TESTS
F:ANOVA(
13-25
Ans
Returns the last answer.
y [ANS]
1-18
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
augment(matrixA,matrixB) Returns a matrix, which is
Ž
matrixB appended to matrixA MATH
as new columns.
7:augment(
10-14
augment(listA,listB)
Returns a list, which is listB
concatenated to the end of
listA.
y [LIST]
OPS
9:augment(
11-15
3-14
3-14
1-12
AxesOff
Turns off the graph axes.
† y [FORMAT]
AxesOff
AxesOn
Turns on the graph axes.
† y [FORMAT]
AxesOn
a+bi
Sets the mode to rectangular
complex number mode (a+bi).
† z
a+bi
bal(npmt[,roundvalue])
Computes the balance at npmt y [FINANCE]
for an amortization schedule
CALC
using stored values for PV, æ, 9:bal(
and PMT and rounds the
computation to roundvalue.
14-9
binomcdf(numtrials,p[,x]) Computes a cumulative
y [DISTR]
probability at x for the discrete DISTR
binomial distribution with the A:binomcdf(
specified numtrials and
probability p of success on
each trial.
13-33
13-33
13-31
binompdf(numtrials,p[,x]) Computes a probability at x for y [DISTR]
the discrete binomial
DISTR
distribution with the specified 0:binompdf(
numtrials and probability p of
success on each trial.
2
c cdf(lowerbound,
Computes the c2 distribution
probability between
lowerbound and upperbound
for the specified degrees of
freedom df.
y [DISTR]
upperbound,df)
DISTR
2
7:c cdf(
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2
c pdf(x,df)
Computes the probability
y [DISTR]
density function (pdf) for the
DISTR
c2 distribution at a specified x 6:c pdf(
value for the specified degrees
of freedom df.
2
13-31
13-22
8-11
2
c .Test(observedmatrix,
Performs a chi-square test.
drawflag=1 draws results;
drawflag=0 calculates results.
† …
expectedmatrix
[,drawflag])
TESTS
2
C:c .Test(
Circle(X,Y,radius)
Clear Entries
ClrAllLists
Draws a circle with center
y [DRAW]
DRAW
9:Circle(
(X,Y) and radius.
Clears the contents of the Last y [MEM]
Entry storage area.
MEMORY
3:Clear Entries 18-4
Sets to 0 the dimension of all
lists in memory.
y [MEM]
MEMORY
4:ClrAllLists
18-4
ClrDraw
Clears all drawn elements from y [DRAW]
a graph or drawing.
DRAW
1:ClrDraw
8-4
ClrHome
Clears the home screen.
†
I/O
8:ClrHome 16-20
ClrList listname1
[,listname2, ...,
listname n]
Sets to 0 the dimension of one
…
EDIT
4:ClrList
or more listnames.
12-20
16-20
2-18
ClrTable
Clears all values from the
table.
†
I/O
9:ClrTable
conj(value)
Connected
Returns the complex conjugate
of a complex number or list of CPX
complex numbers.
1:conj(
Sets connected plotting mode; † z
resets all Y= editor graph-style
Connected
settings to ç .
1-11
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
CoordOff
CoordOn
cos(value)
Turns off cursor coordinate
value display.
Turns on cursor coordinate
value display.
Returns cosine of a
real number, expression, or
list.
Returns arccosine of a real
number, expression, or list.
† y [FORMAT]
CoordOff
3-14
† y [FORMAT]
CoordOn
3-14
™
2-3
L1
L1
cos (value)
y [COS ]
2-3
cosh(value)
Returns hyperbolic cosine of a y [CATALOG]
real number, expression, or
list.
cosh(
15-10
L1
cosh (value)
Returns hyperbolic arccosine
of a real number, expression,
or list.
y [CATALOG]
L1
cosh (
15-10
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
12-26
cumSum(list)
Returns a list of the cumulative y [LIST]
sums of the elements in list,
OPS
starting with the first element. 6:cumSum(
11-12
cumSum(matrix)
Returns a matrix of the
cumulative sums of matrix
Ž
MATH
elements. Each element in the 0:cumSum(
returned matrix is a cumulative
sum of a matrix column from
top to bottom.
10-15
14-13
2-5
dbd(date1,date2)
Calculates the number of days y [FINANCE]
between date1 and date2 using CALC
the actual-day-count method.
D:dbd(
value4Dec
Displays a real or complex
number, expression, list, or
matrix in decimal format.
MATH
2:4Dec
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Degree
Sets degree angle mode.
† z
Degree
1-11
DelVar variable
Deletes from memory the
contents of variable.
†
CTL
G:DelVar
16-15
DependAsk
DependAuto
Sets table to ask for
† y [TBLSET]
dependent-variable values.
Depend: Ask
7-3
Sets table to generate
dependent-variable values
automatically.
† y [TBLSET]
Depend: Auto
7-3
10-12
12-23
12-23
11-11
10-12
11-11
10-13
16-18
16-18
det(matrix)
Returns determinant of
Ž
MATH
1:det(
matrix.
2
DiagnosticOff
Sets diagnostics-off mode; r, r , y [CATALOG]
2
and R are not displayed as
DiagnosticOff
regression model results.
2
DiagnosticOn
Sets diagnostics-on mode; r, r , y [CATALOG]
2
and R are displayed as
DiagnosticOn
regression model results.
dim(listname)
Returns the dimension of
listname.
y [LIST]
OPS
3:dim(
dim(matrixname)
length!dim(listname)
Returns the dimension of
matrixname as a list.
Ž
MATH
3:dim(
Assigns a new dimension
(length) to a new or existing
listname.
y [LIST]
OPS
3:dim(
{rows,columns}!
dim(matrixname)
Assigns new dimensions to a
new or existing matrixname. MATH
Ž
3:dim(
Disp
Displays the home screen.
Displays each value.
†
I/O
3:Disp
Disp [valueA,valueB,
valueC,...,value n]
†
I/O
3:Disp
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
DispGraph
Displays the graph.
†
I/O
4:DispGraph 16-19
DispTable
Displays the table.
†
I/O
5:DispTable 16-19
value4DMS
Displays value in DMS format. y [ANGLE]
ANGLE
4:4DMS
2-24
1-11
8-9
Dot
Sets dot plotting mode; resets
† z
all Y= editor graph-style settings Dot
to í .
DrawF expression
DrawInv expression
Draws expression (in terms of y [DRAW]
X) on the graph.
DRAW
6:DrawF
Draws the inverse of
y [DRAW]
expression by plotting X values DRAW
on the y-axis and Y values on
the x-axis.
8:DrawInv
8-9
:DS<(variable,value)
:commandA
Decrements variable by 1;
skips commandA if variable <
value.
†
CTL
B:DS<(
:commands
16-14
2-4
x
e^(power)
Returns e raised to power.
y [e ]
x
e^(list)
Returns a list of e raised to a
list of powers.
y [e ]
2-4
Exponent:
valueEexponent
Returns value times 10 to the
exponent.
y [EE]
1-7
Exponent:
listEexponent
Returns list elements times 10 y [EE]
to the exponent.
1-7
Exponent:
matrixEexponent
Returns matrix elements times y [EE]
10 to the exponent.
1-7
4Eff(nominal rate,
compounding periods)
Computes the effective interest y [FINANCE]
rate.
CALC
C:4Eff(
14-12
Else
See If:Then:Else
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
End
Identifies end of For(,
If-Then-Else, Repeat, or While
loop.
†
CTL
7:End
16-12
Eng
Sets engineering display mode. † z
Eng
1-10
Equ4String(Y= var,Strn)
Converts the contents of a Y= y [CATALOG]
var to a string and stores it in Equ4String(
Strn.
15-7
expr(string)
Converts string to an
expression and executes it.
y [CATALOG]
expr(
15-7
ExpReg [Xlistname,
Ylistname,freqlist,regequ] model to Xlistname and
Ylistname with frequency
Fits an exponential regression
…
CALC
0:ExpReg
freqlist, and stores the
regression equation to regequ.
12-26
3-14
3-14
ExprOff
ExprOn
Turns off the expression
† y [FORMAT]
display during TRACE.
ExprOff
Turns on the expression
display during TRACE.
† y [FORMAT]
ExprOn
Ücdf(lowerbound,
upperbound,
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]
DISTR
9:Ûcdf(
13-32
10-13
Fill(value,matrixname)
Fill(value,listname)
Fix #
Stores value to each element in Ž
matrixname.
MATH
4:Fill(
Stores value to each element in y [LIST]
listname.
OPS
4:Fill(
11-11
Sets fixed-decimal mode for # † z
of decimal places.
0123456789
(select one) 1-10
Float
Sets floating decimal mode.
† z
Float
1-10
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
fMax(expression,variable, Returns the value of variable
lower,upper[,tolerance]) where the local maximum of
expression occurs, between
MATH
7:fMax(
lower and upper, with
specified tolerance.
2-6
fMin(expression,variable, Returns the value of variable
lower,upper[,tolerance]) where the local minimum of
expression occurs, between
MATH
6:fMin(
lower and upper, with
specified tolerance.
2-6
fnInt(expression,variable, Returns the function integral of
lower,upper[,tolerance]) expression with respect to
variable, between lower and
upper, with specified
MATH
9:fnInt(
tolerance.
2-7
3-8
3-8
FnOff [function#,
Deselects all Y= functions or
Y-VARS On/Off
2:FnOff
function#,...,function n] specified Y= functions.
FnOn [function#,
Selects all Y= functions or
Y-VARS On/Off
1:FnOn
function#,...,function n] specified Y= functions.
:For(variable,begin,end
[,increment])
:commands
Executes commands through †
End, incrementing variable
from begin by increment until
variable>end.
CTL
4:For(
:End
:commands
16-10
fPart(value)
Returns the fractional part or
parts of a real or complex
number, expression, list, or
matrix.
NUM
4:fPart(
2-14
10-11
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]
DISTR
8:Ûpdf(
13-32
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
value4Frac
Displays a real or complex
number, expression, list, or
matrix as a fraction simplified
to its simplest terms.
MATH
1:4Frac
2-5
Full
Sets full screen mode.
† z
Full
1-12
Func
Sets function graphing mode. † z
Func
1-11
gcd(valueA,valueB)
Returns the greatest common
divisor of valueA and valueB, NUM
which can be real numbers or 9:gcd(
lists.
2-15
geometcdf(p,x)
Computes a cumulative
y [DISTR]
probability at x, the number of DISTR
the trial on which the first
success occurs, for the discrete
geometric distribution with the
specified probability of success
p.
E:geometcdf(
13-34
geometpdf(p,x)
Computes a probability at x, the y [DISTR]
number of the trial on which the DISTR
first success occurs, for the
discrete geometric distribution
with the specified probability of
success p.
D:geometpdf(
13-34
16-21
16-21
16-20
16-13
Get(variable)
GetCalc(variable)
getKey
Gets data from the CBL 2/CBL †
System or CBR and stores it in
I/O
variable.
A:Get(
Gets contents of variable on
another TI.83 and stores it to
variable on the receiving TI.83.
†
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
A-10 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
GraphStyle(function#,
graphstyle#)
Sets a graphstyle for
function#.
†
CTL
H:GraphStyle(
16-15
GridOff
GridOn
G-T
Turns off grid format.
Turns on grid format.
† y [FORMAT]
GridOff
3-14
3-14
1-12
1-12
† y [FORMAT]
GridOn
Sets graph-table vertical
split-screen mode.
Sets horizontal
split-screen mode.
† z
G-T
Horiz
† z
Horiz
Horizontal y
Draws a horizontal line at y.
y [DRAW]
DRAW
3:Horizontal
8-6
10-13
16-9
identity(dimension)
Returns the identity matrix of
Ž
dimension rows × dimension MATH
columns.
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
16-9
: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
16-10
imag(value)
Returns the imaginary
(nonreal) part of a complex
number or list of complex
numbers.
CPX
3:imag(
2-18
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
IndpntAsk
Sets table to ask for
independent-variable values.
† y [TBLSET]
Indpnt: Ask
7-3
7-3
IndpntAuto
Sets table to generate
independent-variable values
automatically.
† y [TBLSET]
Indpnt: Auto
Input
Displays graph.
†
I/O
1:Input
16-16
16-17
16-17
15-7
Input [variable]
Input ["text",variable]
Prompts for value to store to
†
I/O
1:Input
variable.
Input [Strn,variable]
Displays Strn and stores
entered value to variable.
†
I/O
1:Input
inString(string,substring
[,start])
Returns the character position y [CATALOG]
in string of the first character inString(
of substring beginning at start.
int(value)
Returns the largest integer a
real or complex number,
expression, list, or matrix.
NUM
5:int(
2-14
10-11
GInt(pmt1,pmt2
[,roundvalue])
Computes the sum, rounded to y [FINANCE]
roundvalue, of the interest
amount between pmt1 and
pmt2 for an amortization
schedule.
CALC
A:GInt(
14-9
invNorm(area[,m,s])
Computes the inverse
y [DISTR]
cumulative normal distribution DISTR
function for a given area under 3:invNorm(
the normal distribution curve
specified by m and s.
13-30
iPart(value)
Returns the integer part of a
real or complex number,
expression, list, or matrix.
NUM
3:iPart(
2-14
10-11
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
irr(CF0,CFList[,CFFreq])
Returns the interest rate at
y [FINANCE]
which the net present value of CALC
the cash flows is equal to zero. 8:irr(
14-8
:IS>(variable,value)
:commandA
:commands
Increments variable
by 1; skips commandA if
variable>value.
†
CTL
A:IS>(
16-13
Ùlistname
Identifies the next one to five
characters as a user-created
list name.
y [LIST]
OPS
B:Ù
11-16
3-14
3-14
LabelOff
LabelOn
Lbl label
Turns off axes labels.
† y [FORMAT]
LabelOff
Turns on axes labels.
† y [FORMAT]
LabelOn
Creates a label of one or two
characters.
†
CTL
9:Lbl
16-13
lcm(valueA,valueB)
Returns the least common
multiple of valueA and valueB, NUM
which can be real numbers or 8:lcm(
lists.
2-15
length(string)
Returns the number of
characters in string.
y [CATALOG]
length(
15-8
Line(X1,Y1,X2,Y2)
Draws a line from (X1,Y1) to
(X2,Y2).
y [DRAW]
DRAW
2:Line(
8-5
Line(X1,Y1,X2,Y2,0)
Erases a line from (X1,Y1) to
(X2,Y2).
y [DRAW]
DRAW
2:Line(
8-5
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
LinReg(a+bx) [Xlistname, Fits a linear regression model
…
CALC
8:LinReg(a+bx)
Ylistname,freqlist,
to Xlistname and Ylistname
with frequency freqlist, and
stores the regression equation
to regequ.
regequ]
12-26
LinReg(ax+b) [Xlistname, Fits a linear regression model
…
CALC
4:LinReg(ax+b)
Ylistname,freqlist,
to Xlistname and Ylistname
with frequency freqlist, and
stores the regression equation
to regequ.
regequ]
12-25
LinRegTTest [Xlistname,
Ylistname,freqlist,
alternative,regequ]
Performs a linear regression
and a t-test. alternative=L1 is
<; alternative=0 is ƒ;
† …
TESTS
E:LinRegTTest
13-24
alternative=1 is >.
@List(list)
Returns a list containing the
differences between
consecutive elements in list.
y [LIST]
OPS
7:@List(
11-12
List 4 matr(listname1,...,
Fills matrixname column by
y [LIST]
listname n,matrixname) column with the elements from OPS
each specified listname.
0:List4 matr(
10-14
11-15
ln(value)
Returns the natural logarithm
of a real or complex number,
expression, or list.
µ
2-4
LnReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a logarithmic regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
…
CALC
9:LnReg
regression equation to regequ.
12-26
log(value)
Returns logarithm of a real or
complex number, expression,
or list.
«
2-4
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
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
12-27
Matr 4 list(matrix,
Fills each listname with
y [LIST]
listnameA,...,listname n) elements from each column in OPS
10-14
11-16
matrix.
A:Matr 4 list(
Matr 4 list(matrix,
column#,listname)
Fills a listname with elements y [LIST]
from a specified column# in
OPS
10-14
11-16
matrix.
A:Matr 4 list(
max(valueA,valueB)
max(list)
Returns the larger of valueA
NUM
7:max(
and valueB.
2-15
Returns largest real or
complex element in list.
y [LIST]
MATH
2:max(
11-16
max(listA,listB)
Returns a real or complex list of y [LIST]
the larger of each pair of
MATH
elements in listA and listB.
2:max(
11-16
11-16
11-16
11-16
max(value,list)
Returns a real or complex list of y [LISTä
the larger of value or each list MATH
element.
2:max(
mean(list[,freqlist])
median(list[,freqlist])
Returns the mean of list with
frequency freqlist.
y [LIST]
MATH
3:mean(
Returns the median of list with y [LIST]
frequency freqlist.
MATH
4:median(
Med-Med [Xlistname,
Ylistname,freqlist,
regequ]
Fits a median-median model to …
Xlistname and Ylistname with CALC
frequency freqlist, and stores
the regression equation to
regequ.
3:Med-Med
12-25
Menu("title","text1",label1 Generates a menu of up to
†
CTL
C:Menu(
[,...,"text7",label7])
seven items during program
execution.
16-14
Tables and Reference Information A-15
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
min(valueA,valueB)
Returns smaller of valueA and
valueB.
NUM
6:min(
2-15
11-16
11-16
11-16
2-21
min(list)
Returns smallest real or
y [LIST]
MATH
1:min(
complex element in list.
min(listA,listB)
min(value,list)
valueA nCr valueB
value nCr list
list nCr value
listA nCr listB
Returns real or complex list of y [LIST]
the smaller of each pair of
MATH
1:min(
elements in listA and listB.
Returns a real or complex list y [LIST]
of the smaller of value or each MATH
list element.
Returns the number of
combinations of valueA taken PRB
valueB at a time.
1:min(
3:nCr
Returns a list of the
PRB
combinations of value taken
each element in list at a time. 3:nCr
2-21
Returns a list of the
combinations of each element PRB
in list taken value at a time.
3:nCr
2-21
Returns a list of the
combinations of each element PRB
in listA taken each element in 3:nCr
listB at a time.
2-21
nDeriv(expression,variable, Returns approximate
MATH
8:nDeriv(
value[,H])
numerical derivative of
expression with respect to
variable at value, with
specified H.
2-7
4Nom(effective rate,
compounding periods)
Computes the nominal interest y [FINANCE]
rate.
CALC
B:4Nom(
14-12
Normal
Sets normal display mode.
† z
Normal
1-10
A-16 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
normalcdf(lowerbound,
upperbound[,m,s])
Computes the normal
distribution probability
between lowerbound and
upperbound for the specified m
and s.
y [DISTR]
DISTR
2:normalcdf(
13-27
normalpdf(x[,m,s])
Computes the probability
y [DISTR]
density function for the normal DISTR
distribution at a specified x
value for the specified m and s.
1:normalpdf(
13-29
2-26
2-21
2-21
2-21
not(value)
Returns 0 if value is ƒ 0. value y [TEST]
can be a real number,
expression, or list.
LOGIC
4:not(
valueA nPr valueB
value nPr list
list nPr value
listA nPr listB
Returns the number of
permutations of valueA taken PRB
valueB at a time.
2:nPr
Returns a list of the
PRB
permutations of value taken
each element in list at a time. 2:nPr
Returns a list of the
permutations of each element PRB
in list taken value at a time.
2:nPr
Returns a list of the
permutations of each element PRB
in listA taken each element in 2:nPr
listB at a time.
2-21
npv(interest rate,CF0,
CFList[,CFFreq])
Computes the sum of the
y [FINANCE]
present values for cash inflows CALC
and outflows.
7:npv(
14-8
valueA or valueB
Returns 1 if valueA or valueB y [TEST]
is ƒ 0. valueA and valueB can LOGIC
be real numbers, expressions, 2:or
or lists.
2-26
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Output(row,column,"text") Displays text beginning at
†
I/O
specified row and column.
6:Output(
16-19
Output(row,column,value) Displays value beginning at
†
I/O
specified row and column.
6:Output(
16-19
Param
Pause
Sets parametric graphing
mode.
Suspends program execution
until you press Í.
† z
Par
1-11
†
CTL
8:Pause
16-12
Pause [value]
Displays value; suspends
program execution until you
press Í.
†
CTL
8:Pause
16-12
Plot#(type,Xlistname,
Ylistname,mark)
Defines Plot# (1, 2, or 3) of
type Scatter or xyLine for
Xlistname and Ylistname
using mark.
† y [STAT PLOT]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
12-37
Plot#(type,Xlistname,
freqlist)
Defines Plot# (1, 2, or 3) of
type Histogram or Boxplot for
Xlistname with frequency
freqlist.
† y [STAT PLOT]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
12-37
Plot#(type,Xlistname,
freqlist,mark)
Defines Plot# (1, 2, or 3) of
type ModBoxplot for
Xlistname with frequency
freqlist using mark.
† y [STAT PLOT]
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
12-37
Plot#(type,datalistname,
data axis,mark)
Defines Plot# (1, 2, or 3) of
type NormProbPlot for
† y [STAT PLOT]
PLOTS
1:Plot1(
datalistname on data axis
using mark. data axis can be X 2:Plot2(
or Y.
3:Plot3(
12-37
12-35
12-35
PlotsOff [1,2,3]
Deselects all stat plots or one y [STAT PLOT]
or more specified stat plots (1, STAT PLOTS
2, or 3).
4:PlotsOff
PlotsOn [1,2,3]
Selects all stat plots or one or y [STAT PLOT]
more specified stat plots (1, 2, STAT PLOTS
or 3).
5:PlotsOn
A-18 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Pmt_Bgn
Specifies an annuity due,
where payments occur at the
beginning of each payment
period.
y [FINANCE]
CALC
F:Pmt_Bgn
14-13
Pmt_End
Specifies an ordinary annuity,
where payments occur at the
end of each payment period.
y [FINANCE]
CALC
E:Pmt_End
14-13
poissoncdf(m,x)
Computes a cumulative
y [DISTR]
probability at x for the discrete DISTR
Poisson distribution with
specified mean m.
C:poissoncdf(
13-34
poissonpdf(m,x)
Computes a probability at x for y [DISTR]
the discrete Poisson distribution DISTR
with the specified mean m.
B:poissonpdf( 13-33
Polar
Sets polar graphing mode.
† z
Pol
1-11
complex value 4Polar
Displays complex value in
polar format.
CPX
7:4Polar
2-19
PolarGC
Sets polar graphing
coordinates format.
† y [FORMAT]
PolarGC
3-13
prgmname
Executes the program name.
†
CTRL
D:prgm
16-15
GPrn(pmt1,pmt2
[,roundvalue])
Computes the sum, rounded to y [FINANCE]
roundvalue, of the principal
amount between pmt1 and
pmt2 for an amortization
schedule.
CALC
0:GPrn(
14-9
11-18
16-18
prod(list[,start,end])
Returns product of list
elements between start and
end.
y [LIST]
MATH
6:prod(
Prompt variableA
[,variableB,...,variable n] variableA, then variableB, and
Prompts for value for
†
I/O
2:Prompt
so on.
Tables and Reference Information A-19
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
1.PropZInt(x,n
[,confidence level])
Computes a one-proportion
z confidence interval.
† …
TESTS
A:1.PropZInt( 13-20
2.PropZInt(x1,n1,x2,n2
[,confidence level])
Computes a two-proportion
z confidence interval.
† …
TESTS
B:2.PropZInt( 13-21
1.PropZTest(p0,x,n
[,alternative,drawflag])
Computes a one-proportion
z test. alternative=L1 is <;
alternative=0 is ƒ;
† …
TESTS
5:1.PropZTest(
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-14
2.PropZTest(x1,n1,x2,n2
[,alternative,drawflag])
Computes a two-proportion
z test. alternative=L1 is <;
alternative=0 is ƒ;
† …
TESTS
6:2.PropZTest(
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-15
Pt.Change(x,y)
Reverses a point at (x,y).
y [DRAW]
POINTS
3:Pt.Change(
8-15
8-15
8-14
Pt.Off(x,y[,mark])
Pt.On(x,y[,mark])
Erases a point at (x,y) using
y [DRAW]
POINTS
2:Pt.Off(
mark.
Draws a point at (x,y) using
mark.
y [DRAW]
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
12-27
A-20 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Pxl.Change(row,column)
Pxl.Off(row,column)
Pxl.On(row,column)
pxl.Test(row,column)
Reverses pixel at
(row,column); 0 row 62
and 0 column 94.
Erases pixel at (row,column); y [DRAW]
0 row 62 and
0 column 94.
y [DRAWä
POINTS
6:Pxl.Change( 8-16
POINTS
5:Pxl.Off(
8-16
Draws pixel at (row,column); y [DRAW]
0 row 62 and
0 column 94.
POINTS
4:Pxl.On(
8-16
Returns 1 if pixel (row,
column) is on, 0 if it is off;
0 row 62 and
y [DRAW]
POINTS
7:pxl.Test(
0 column 94.
8-16
2-24
2-24
P4Rx(r,q)
Returns X, given polar
y [ANGLE]
coordinates r and q or a list of ANGLE
polar coordinates.
7:P4Rx(
P4Ry(r,q)
Returns Y, given polar
y [ANGLE]
coordinates r and q or a list of ANGLE
polar coordinates.
8:P4Ry(
QuadReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a quadratic regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
…
CALC
5:QuadReg
regression equation to regequ.
12-25
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
12-26
Radian
Sets radian angle mode.
† z
Radian
1-11
rand[(numtrials)]
Returns a random number
between 0 and 1 for a
specified number of trials
numtrials.
PRB
1:rand
2-20
randBin(numtrials,prob
[,numsimulations])
Generates and displays a
PRB
random real number from a
specified Binomial distribution. 7:randBin(
2-22
Tables and Reference Information A-21
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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 PRB
specified by lower and upper
integer bounds for a specified
number of trials numtrials.
5:randInt(
2-22
randM(rows,columns)
Returns a random matrix of
Ž
rows (1–99) × columns (1–99). MATH
6:randM(
10-13
randNorm(m,s[,numtrials]) Generates and displays a
PRB
random real number from a
specified Normal distribution 6:randNorm(
specified by m and s for a
specified number of trials
numtrials.
2-22
re^qi
Sets the mode to polar
† z
complex number mode (re^qi). re^qi
1-12
Real
Sets mode to display complex † z
results only when you enter
complex numbers.
Real
1-12
2-18
8-20
8-18
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 y [DRAW]
the graph database variable
STO
4:RecallGDB
GDBn.
Displays the graph and adds
the picture stored in Picn.
y [DRAW]
STO
2:RecallPic
complex value 4Rect
Displays complex value or list
in rectangular format.
CPX
6:4Rect
2-19
RectGC
Sets rectangular graphing
coordinates format.
† y [FORMAT]
RectGC
3-13
ref(matrix)
Returns the row-echelon form
of a matrix.
Ž
MATH
A:ref(
10-15
A-22 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
:Repeat condition
:commands
:End
Executes commands until
condition is true.
†
CTL
6:Repeat
16-11
:commands
Return
Returns to the calling program. †
CTL
E:Return
16-15
2-13
round(value[,#decimals])
ärow(value,matrix,row)
Returns a number, expression,
list, or matrix rounded to
#decimals ( 9).
NUM
2:round(
Returns a matrix with row of
Ž
matrix multiplied by value and MATH
stored in row.
E:ärow(
10-16
10-16
row+(matrix,rowA,rowB) Returns a matrix with rowA of
matrix added to rowB and
Ž
MATH
D:row+(
stored in rowB.
ärow+(value,matrix,
rowA,rowB)
Returns a matrix with rowA of
matrix multiplied by value,
added to rowB, and stored in
rowB.
Ž
MATH
F:ärow+(
10-16
10-16
10-15
2-24
rowSwap(matrix,rowA,
Returns a matrix with rowA of
Ž
MATH
C:rowSwap(
rowB)
matrix swapped with rowB.
rref(matrix)
R4Pr(x,y)
Returns the reduced row-
echelon form of a matrix.
Ž
MATH
B:rref(
Returns R, given rectangular
y [ANGLE]
coordinates x and y or a list of ANGLE
rectangular coordinates.
5:R4Pr(
R4Pq(x,y)
Returns q, given rectangular
y [ANGLE]
coordinates x and y or a list of ANGLE
rectangular coordinates.
6:R4Pq(
2-24
Tables and Reference Information A-23
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2.SampÜTest [listname1, Performs a two-sample Û test. † …
listname2,freqlist1,
freqlist2,alternative,
drawflag]
alternative=L1 is <;
TESTS
D:2.SampÛTest
alternative=0 is ƒ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
(Data list input)
13-23
2.SampÜTest Sx1,n1,
Sx2,n2[,alternative,
drawflag]
Performs a two-sample Û test. † …
alternative=L1 is <;
TESTS
D:2.SampÛTest
alternative=0 is ƒ;
(Summary stats input)
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-23
2.SampTInt [listname1,
listname2,
Computes a two-sample t
confidence interval. pooled=1
pools variances; pooled=0 does
† …
TESTS
freqlist1,freqlist2,
0:2.SampTInt
confidence level,pooled] not pool variances.
(Data list input)
13-19
2.SampTInt v1,Sx1,n1,
Computes a two-sample t
confidence interval. pooled=1
† …
v2,Sx2,n2
TESTS
[,confidence level,pooled] pools variances; pooled=0 does
(Summary stats input)
0:2.SampTInt
not pool variances.
13-19
2.SampTTest [listname1, Computes a two-sample t test. † …
listname2,freqlist1,
freqlist2,alternative,
pooled,drawflag]
alternative=L1 is <;
TESTS
4:2.SampTTest
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)
13-13
A-24 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
2.SampTTest v1,Sx1,n1,
v2,Sx2,n2[,alternative,
pooled,drawflag]
Computes a two-sample t test. † …
alternative=L1 is <;
TESTS
alternative=0 is ƒ;
4:2.SampTTest
(Summary stats input)
alternative=1 is >. pooled=1
pools variances; pooled=0 does
not pool variances. drawflag=1
draws results; drawflag=0
calculates results.
13-13
2.SampZInt(s1,s2
[,listname1,listname2,
freqlist1,freqlist2,
confidence level])
(Data list input)
Computes a two-sample z
confidence interval.
† …
TESTS
9:2.SampZInt(
13-18
2.SampZInt(s1,s2,
v1,n1,v2,n2
[,confidence level])
(Summary stats input)
Computes a two-sample z
confidence interval.
† …
TESTS
9:2.SampZInt(
13-18
2.SampZTest(s1,s2
[,listname1,listname2,
freqlist1,freqlist2,
alternative,drawflag])
(Data list input)
Computes a two-sample z test. † …
alternative=L1 is <;
TESTS
3:2.SampZTest(
alternative=0 is ƒ ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-12
2.SampZTest(s1,s2,
v1,n1,v2,n2
[,alternative,drawflag])
(Summary stats input)
Computes a two-sample z test. † …
alternative=L1 is <;
TESTS
3:2.SampZTest(
alternative=0 is ƒ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-12
Sci
Sets scientific notation display † z
mode.
Sci
1-10
Select(Xlistname,
Ylistname)
Selects one or more specific
y [LIST]
data points from a scatter plot OPS
or xyLine plot (only), and then 8:Select(
stores the selected data points
to two new lists, Xlistname
and Ylistname.
11-12
Tables and Reference Information A-25
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Send(variable)
Sends contents of variable to †
the CBL 2/CBL System or CBR.
I/O
B:Send(
16-21
seq(expression,variable,
begin,end[,increment])
Returns list created by
y [LIST]
evaluating expression with
OPS
regard to variable, from begin 5:seq(
to end by increment.
11-11
1-11
1-12
Seq
Sets sequence graphing mode. † z
Seq
Sequential
SetUpEditor
Sets mode to graph functions † z
sequentially.
Sequential
Removes all list names from
the stat list editor, and then
…
EDIT
restores list names L1 through 5:SetUpEditor
L6 to columns 1 through 6.
12-21
SetUpEditor listname1
[,listname2,...,
listname20]
Removes all list names from
…
the stat list editor, then sets it EDIT
up to display one or more
listnames in the specified
order, starting with column 1.
5:SetUpEditor
12-21
Shade(lowerfunc,
Draws lowerfunc and
y [DRAW]
upperfunc[,Xleft,Xright, upperfunc in terms of X on the DRAW
pattern,patres])
current graph and uses
7:Shade(
pattern and patres to shade the
area bounded by lowerfunc,
upperfunc, Xleft, and Xright.
8-10
2
Shadec (lowerbound,
Draws the density function for y [DISTR]
upperbound,df)
the c2 distribution specified by DRAW
2
degrees of freedom df and
shades the area between
lowerbound and upperbound.
3:Shadec (
13-36
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
ShadeÜ(lowerbound,
upperbound,
Draws the density function for y [DISTR]
the Û distribution specified by DRAW
numerator df,
numerator df and
4:ShadeÜ(
denominator df)
denominator df and shades the
area between lowerbound and
upperbound.
13-36
ShadeNorm(lowerbound,
upperbound[,m,s])
Draws the normal density
function specified by m and s
and shades the area between
lowerbound and upperbound.
y [DISTR]
DRAW
1:ShadeNorm(
13-35
Shade_t(lowerbound,
upperbound,df)
Draws the density function for y [DISTR]
the Student-t distribution
specified by degrees of
freedom df, and shades the
area between lowerbound and
upperbound.
DRAW
2:Shade_t(
13-36
1-12
2-3
Simul
Sets mode to graph functions † z
simultaneously.
Simul
sin(value)
Returns the sine of a real
number, expression, or list.
˜
L1
L1
sin (value)
Returns the arcsine of a real
number, expression, or list.
y [SIN ]
2-3
sinh(value)
Returns the hyperbolic sine of y [CATALOG]
a real number, expression, or
list.
sinh(
15-10
L1
sinh (value)
Returns the hyperbolic arcsine y [CATALOG]
L1
of a real number, expression,
or list.
sinh (
15-10
Tables and Reference Information A-27
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
SinReg [iterations,
Xlistname,Ylistname,
period,regequ]
Attempts iterations times to fit
…
a sinusoidal regression model to CALC
Xlistname and Ylistname using C:SinReg
a period guess, and stores the
regression equation to regequ.
12-27
solve(expression,variable, Solves expression for variable, †
guess,{lower,upper})
given an initial guess and lower MATH
and upper bounds within
0:solve(
which the solution is sought.
2-12
SortA(listname)
Sorts elements of listname in y [LIST]
ascending order.
OPS
11-10
12-20
1:SortA(
SortA(keylistname,
Sorts elements of keylistname y [LIST]
dependlist1[,dependlist2, in ascending order, then sorts OPS
...,dependlist n])
each dependlist as a dependent 1:SortA(
list.
11-10
12-20
SortD(listname)
Sorts elements of listname in y [LIST]
descending order.
OPS
11-10
12-20
2:SortD(
SortD(keylistname,
Sorts elements of keylistname y [LIST]
in descending order, then sorts OPS
dependlist1[,dependlist2,..., each dependlist as a dependent 2:SortD(
dependlist n])
11-10
12-20
list.
stdDev(list[,freqlist])
Returns the standard deviation y [LIST]
of the elements in list with
MATH
frequency freqlist.
7:stdDev(
11-18
Stop
Ends program execution;
returns to home screen.
†
CTL
F:Stop
16-15
Store: value!variable
Stores value in variable.
¿
1-14
StoreGDB n
Stores current graph in
database GDBn.
y [DRAW]
STO
3:StoreGDB
8-19
A-28 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
StorePic n
Stores current picture in
picture Picn.
y [DRAW]
STO
1:StorePic
8-17
15-8
15-9
11-18
2-3
String4Equ(string,Y= var) Converts string into an
y [CATALOG]
equation and stores it in Y=
String4Equ(
var.
sub(string,begin,length)
sum(list[,start,end])
tan(value)
Returns a string that is a subset y [CATALOG]
of another string, from begin sub(
to length.
Returns the sum of elements of y [LIST]
list from start to end.
MATH
5:sum(
Returns the tangent of a real
number, expression,
or list.
Returns the arctangent of a
real number, expression, or
list.
š
L1
L1
tan (value)
y [TAN ]
2-3
Tangent(expression,value) Draws a line tangent to
y [DRAWä
DRAW
5:Tangent(
expression at X=value.
8-8
tanh(value)
Returns hyperbolic tangent of a y [CATALOG]
real number, expression, or list. tanh(
15-10
L1
tanh (value)
Returns the hyperbolic
arctangent of a real number,
expression,
y [CATALOG]
L1
tanh (
or list.
15-10
tcdf(lowerbound,
upperbound,df)
Computes the Student-t
distribution probability
between lowerbound and
upperbound for the specified
degrees of freedom df.
y [DISTR]
DISTR
5:tcdf(
13-31
Text(row,column,text1,
text2,...,text n)
Writes text on graph beginning y [DRAW]
at pixel (row,column), where DRAW
0 row 57 and
0:Text(
0 column 94.
8-12
Then
See If:Then
Tables and Reference Information A-29
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Time
Sets sequence graphs to plot
with respect to time.
† y [FORMAT]
Time
6-8
TInterval [listname,
Computes a t confidence
† …
freqlist,confidence level] interval.
TESTS
(Data list input)
8:TInterval 13-17
TInterval v,Sx,n
[,confidence level]
(Summary stats input)
Computes a t confidence
interval.
† …
TESTS
8:TInterval 13-17
tpdf(x,df)
Computes the probability
density function (pdf) for the
Student-t distribution at a
specified x value with specified
degrees of freedom df.
y [DISTR]
DISTR
4:tpdf(
13-30
Trace
Displays the graph and enters
TRACE mode.
r
3-18
T-Test m0[,listname,
freqlist,alternative,
drawflag]
Performs a t test with
frequency freqlist.
† …
TESTS
2:T-Test
alternative=L1 is <;
(Data list input)
alternative=0 is ƒ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-11
T-Test m0, v,Sx,n
[,alternative,drawflag]
(Summary stats input)
Performs a t test with
frequency freqlist.
† …
TESTS
2:T-Test
alternative=L1 is < ;
alternative=0 is ƒ ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-11
A-30 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
tvm_FV[(Ú,æ,PV,PMT,
P/Y,C/Y)]
Computes the future value.
y [FINANCE]
CALC
6:tvm_FV
14-7
14-7
14-7
14-6
14-7
6-8
tvm_æ[(Ú,PV,PMT,FV,
Computes the annual interest y [FINANCE]
P/Y,C/Y)]
rate.
CALC
3:tvm_æ
tvm_Ú[(æ,PV,PMT,FV,
P/Y,C/Y)]
Computes the number of
payment periods.
y [FINANCE]
CALC
5:tvm_Ú
tvm_Pmt[(Ú,æ,PV,FV,
P/Y,C/Y)]
Computes the amount of each y [FINANCE]
payment.
CALC
2:tvm_Pmt
tvm_PV[(Ú,æ,PMT,FV,
P/Y,C/Y)]
Computes the present value.
y [FINANCE]
CALC
4:tvm_PV
uvAxes
uwAxes
Sets sequence graphs to plot
u(n) on the x-axis and v(n) on
the y-axis.
† y [FORMAT]
uv
Sets sequence graphs to plot
u(n) on the x-axis and w(n) on
the y-axis.
† y [FORMAT]
uw
6-8
1-Var Stats [Xlistname,
freqlist]
Performs one-variable analysis …
on the data in Xlistname with CALC
frequency freqlist.
1:1-Var Stats 12-25
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
12-25
11-18
8-6
variance(list[,freqlist])
Vertical x
Returns the variance of the
y [LIST]
elements in list with frequency MATH
freqlist.
Draws a vertical line
at x.
8:variance(
y [DRAW]
DRAW
4:Vertical
vwAxes
Sets sequence graphs to plot
v(n) on the x-axis and w(n) on
the y-axis.
† y [FORMAT]
vw
6-8
Web
Sets sequence graphs to trace † y [FORMAT]
as webs. Web
6-8
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
:While condition
:commands
:End
Executes commands while
condition is true.
†
CTL
5:While
16-11
:command
valueA xor valueB
Returns 1 if only valueA or
y [TEST]
valueB = 0. valueA and valueB LOGIC
can be real numbers,
expressions, or lists.
3:xor
2-26
ZBox
Displays a graph, lets you draw † q
a box that defines a new
viewing window, and updates
the window.
ZOOM
1:ZBox
3-20
ZDecimal
Adjusts the viewing window so † q
that @X=0.1 and @Y=0.1, and
displays the graph screen with
the origin centered on the
screen.
ZOOM
4:ZDecimal
3-21
ZInteger
Redefines the viewing window † q
using these dimensions:
ZOOM
@X=1
Xscl=10
Yscl=10
8:ZInteger
@Y=1
3-22
13-16
13-16
3-21
ZInterval s[,listname,
Computes a z confidence
† …
freqlist,confidence level] interval.
TESTS
(Data list input)
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 † q
that surrounds the cursor
location.
ZOOM
2:Zoom In
Zoom Out
Displays a greater portion of
the graph, centered on the
cursor location.
† q
ZOOM
3:Zoom Out 3-21
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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
† q
ZOOM
0:ZoomFit
selected functions and replots
the functions.
3-22
ZoomRcl
ZoomStat
ZoomSto
ZPrevious
Graphs the selected functions † q
in a user-defined viewing
window.
MEMORY
3:ZoomRcl
3-23
3-22
3-23
Redefines the viewing window † q
so that all statistical data
points are displayed.
ZOOM
9:ZoomStat
Immediately stores the current † q
viewing window.
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
3-23
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
3-21
ZStandard
Replots the functions
immediately, updating the
window variables to the
default values.
† q
ZOOM
6:ZStandard
3-22
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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.
† …
TESTS
1:Z.Test(
alternative=L1 is <;
(Data list input)
alternative=0 is ƒ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-10
ZNTest(m0,s,v,n
Performs a z test.
† …
TESTS
1:Z.Test(
[,alternative,drawflag]) alternative=L1 is <;
(Summary stats input)
alternative=0 is ƒ;
alternative=1 is >. drawflag=1
draws results; drawflag=0
calculates results.
13-10
ZTrig
Replots the functions
immediately, updating the
window variables to preset
values for plotting trig
functions.
† q
ZOOM
7:ZTrig
3-22
Factorial: value!
Factorial: list!
Returns factorial of value.
PRB
4:!
2-21
2-21
2-23
2-24
Returns factorial of list
elements.
PRB
4:!
Degrees notation: value¡
Radian: angler
Interprets value as degrees;
designates degrees in DMS
format.
y [ANGLE]
ANGLE
1:¡
Interprets angle as radians.
y [ANGLE]
ANGLE
r
3:
Transpose: matrixT
Returns a matrix in which each
element (row, column) is
swapped with the
Ž
MATH
T
2:
corresponding element
(column, row) of matrix.
10-12
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
xthrootx‡value
xthrootx‡list
listx‡value
Returns xthroot of value.
MATH
x
5: ‡
2-6
2-6
2-6
2-6
Returns xthroot of list
elements.
MATH
x
5: ‡
Returns list roots of value.
Returns listA roots of listB.
Returns the cube of a real or
MATH
x
5: ‡
listAx‡listB
Cube: value3
MATH
x
5: ‡
complex number, expression, MATH
list, or square matrix.
3
3:
2-6
10-10
Cube root: 3‡(value)
Returns the cube root of a real or
complex number, expression, or MATH
3
list.
4: ‡(
2-6
Equal: valueA=valueB
Returns 1 if valueA = valueB.
y [TEST]
Returns 0 if valueA ƒ valueB.
TEST
valueA and valueB can be real 1:=
or complex numbers,
2-25
10-11
expressions, lists, or matrices.
Not equal: valueAƒvalueB Returns 1 if valueA ƒ valueB.
y [TEST]
Returns 0 if valueA = valueB.
TEST
valueA and valueB can be real 2:ƒ
or complex numbers,
2-25
10-11
expressions, lists, or matrices.
Less than: valueA<valueB Returns 1 if valueA < valueB.
y [TEST]
TEST
Returns 0 if valueA ‚ valueB.
valueA and valueB can be real 5:<
or complex numbers,
expressions, or lists.
2-25
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Greater than:
valueA>valueB
Returns 1 if valueA > valueB.
y [TEST]
Returns 0 if valueA valueB.
TEST
valueA and valueB can be real 3:>
or complex numbers,
expressions, or lists.
2-25
Less than or equal:
valueAvalueB
Returns 1 if valueA valueB.
y [TEST]
TEST
Returns 0 if valueA > valueB.
valueA and valueB can be real 6:
or complex numbers,
expressions, or lists.
2-25
Greater than or equal:
valueA‚valueB
Returns 1 if valueA ‚ valueB.
y [TEST]
TEST
Returns 0 if valueA < valueB.
valueA and valueB can be real 4:‚
or complex numbers,
expressions, or lists.
2-25
Inverse: valueL1
Returns 1 divided by a real or
complex number or
expression.
Returns 1 divided by list
elements.
—
—
2-3
Inverse: listL1
2-3
10-10
Inverse: matrixL1
Square: value2
Returns matrix inverted.
—
¡
Returns value multiplied by
itself. value can be a real or
complex number or
expression.
2-3
2-3
Square: list2
Returns list elements squared.
¡
¡
›
Square: matrix2
Powers: value^power
Returns matrix multiplied by
itself.
Returns value raised to power.
value can be a real or complex
number or expression.
Returns list elements raised to
power.
Returns value raised to list
elements.
10-10
2-3
2-3
2-3
Powers: list^power
›
›
Powers: value^list
A-36 Tables and Reference Information
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Powers: matrix^power
Returns matrix elements
raised to power.
›
10-10
Negation: Lvalue
Returns the negative of a real
or complex number,
Ì
2-4
expression, list, or matrix.
10-9
y [10x]
Power of ten: 10^(value)
Returns 10 raised to the value
power. value can be a real or
complex number or
expression.
Returns a list of 10 raised to
the list power.
2-4
y [10x]
Power of ten: 10^(list)
2-4
Square root: ‡(value)
Returns square root of a real or y [‡]
complex number, expression,
or list.
2-3
2-3
2-3
2-3
2-3
10-9
10-9
2-3
2-3
2-3
2-3
Multiplication:
Returns valueA times valueB.
¯
¯
¯
¯
¯
¯
¥
¥
¥
valueAävalueB
Multiplication:
valueälist
Returns value times each list
element.
Returns each list element
times value.
Returns listA elements times
listB elements.
Returns value times matrix
elements.
Returns matrixA times
matrixB.
Returns valueA divided by
valueB.
Returns list elements divided
by value.
Returns value divided by list
elements.
Multiplication:
listävalue
Multiplication:
listAälistB
Multiplication:
valueämatrix
Multiplication:
matrixAämatrixB
Division: valueAàvalueB
Division: listàvalue
Division: valueàlist
Division: listAàlistB
Returns listA elements divided ¥
by listB elements.
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Function or Instruction/
Arguments
Key or Keys/
Menu or Screen/Item
Result
Addition: valueA+valueB
Addition: list+value
Returns valueA plus valueB.
Returns list in which value is
added to each list element.
Ã
Ã
2-3
2-3
Addition: listA+listB
Returns listA elements plus
Ã
Ã
Ã
¹
¹
¹
¹
¹
listB elements.
2-3
Addition:
matrixA+matrixB
Returns matrixA elements
plus matrixB elements.
Concatenates two or more
strings.
Subtracts valueB from valueA.
10-9
15-6
2-3
Concatenation:
string1+string2
Subtraction:
valueANvalueB
Subtraction:
valueNlist
Subtracts list elements from
value.
Subtracts value from list
elements.
Subtracts listB elements from
listA elements.
Subtracts matrixB elements
from matrixA elements.
2-3
Subtraction:
listNvalue
2-3
Subtraction:
listANlistB
2-3
Subtraction:
matrixANmatrixB
10-9
Minutes notation:
degrees¡minutes'
seconds"
Interprets minutes angle
measurement as minutes.
y [ANGLE]
ANGLE
2:'
2-23
Seconds notation:
degrees¡minutes'
seconds"
Interprets seconds angle
measurement as seconds.
ƒ [ã]
2-23
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TI-83 Menu Map
The TI.83 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)
Plot1 Plot2
Plot3
çY1=
çY2=
çY3=
çY4=
...
çY9=
çY0=
(Par mode)
Plot1 Plot2
Plot3
çX1T=
Y1T=
çX2T=
Y2T=
...
çX6T=
(Pol mode)
Plot1 Plot2
Plot3
çr1=
çr2=
çr3=
çr4=
çr5=
çr6=
(Seq mode)
Plot1 Plot2
Plot3
nMin=1
íu(n)=
u(nMin)=
ív(n)=
v(nMin)=
íw(n)=
w(nMin)=
Y6T=
y [STAT PLOT]
y [STAT PLOT]
ÚÄÄÄÄÄÁÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ÚÄÄÄÄÄÙ
STAT PLOTS
1:Plot1…Off
(PRGM editor) (PRGM editor)
(PRGM editor)
PLOTS
TYPE
1:Scatter
2:xyLine
MARK
1:›
2:+
3:¦
" L1 L2
›
1:Plot1(
2:Plot2(
3:Plot3(
4:PlotsOff
5:PlotsOn
2:Plot2…Off
" L1 L2
›
3:Histogram
4:ModBoxplot
5:Boxplot
6:NormProbPlot
3:Plot3…Off
" L1 L2
4:PlotsOff
5:PlotsOn
›
p
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func mode)
WINDOW
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
(Par mode)
WINDOW
Tmin=0
(Pol mode)
WINDOW
qmin=0
(Seq mode)
WINDOW
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
Ymin=-10
Ymax=10
Yscl=1
Xres=1
y [TBLSET]
y [TBLSET]
ÚÄÄÄÙ
ÚÄÄÄÄÙ
TABLE SETUP
TblStart=0
@Tbl=1
Indpnt:Auto Ask
Depend:Auto Ask
(PRGM editor)
TABLE SETUP
Indpnt:Auto Ask
Depend:Auto Ask
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q
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
ZOOM
1:ZBox
MEMORY
MEMORY
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 [FORMAT]
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(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
y [CALC]
ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func mode)
CALCULATE
1:value
(Par mode)
CALCULATE
1:value
(Pol mode)
CALCULATE
1:value
(Seq mode)
CALCULATE
1:value
2:zero
2:dy/dx
2:dy/dx
3:minimum
4:maximum
5:intersect
6:dy/dx
3:dy/dt
4:dx/dt
3:dr/dq
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
A-40 Tables and Reference Information
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y [LINK]
ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
SEND
1:All+…
RECEIVE
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:Back Up…
…
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
EDIT
1:Edit…
2:SortA(
3:SortD(
4:ClrList
5:SetUpEditor
CALC
TESTS
1:Z-Test…
2:T-Test…
1:1-Var Stats
2:2-Var Stats
3:Med-Med
4:LinReg(ax+b)
5:QuadReg
6:CubicReg
7:QuartReg
8:LinReg(a+bx)
9:LnReg
0:ExpReg
A:PwrReg
B:Logistic
C:SinReg
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…
D:2-SampÛTest…
E:LinRegTTest…
F:ANOVA(
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y [LIST]
ÚÄÄÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
NAMES
OPS
MATH
1:min(
2:max(
3:mean(
4:median(
5:sum(
1:listname
2:listname
3:listname
...
1:SortA(
2:SortD(
3:dim(
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:rand
2:nPr
3:nCr
1:4Frac
2:4Dec
1:abs(
2:round(
3:iPart(
4:fPart(
5:int(
6:min(
7:max(
8:lcm(
9:gcd(
1:conj(
2:real(
3:imag(
4:angle(
5:abs(
6:4Rect
7:4Polar
3
3:
3
4: ‡(
4:!
x‡
5:
5:randInt(
6:randNorm(
7:randBin(
6:fMin(
7:fMax(
8:nDeriv(
9:fnInt(
0:Solver…
y [TEST]
ÚÄÄÁÄÄÄÄÄÄÄÄÄ¿
TEST
1:=
2:ƒ
3:>
4:‚
5:<
6:
LOGIC
1:and
2:or
3:xor
4:not(
A-42 Tables and Reference Information
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Ž
y [ANGLE]
ÚÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
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]
5:[E]
6:[F]
7:[G]
8:[H]
9:[I]
0:[J]
T
2:
2:'
r
3:dim(
4:Fill(
3:
4:4DMS
5:identity(
6:randM(
7:augment(
8:Matr4list(
9:List4matr(
0:cumSum(
A:ref(
5:R4Pr(
6:R4Pq(
7:P4Rx(
8:P4Ry(
B:rref(
C:rowSwap(
D:row+(
E:…row(
F:…row+(
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
EXEC
EDIT
NEW
1:Create New
1:name
2:name
...
1:name
2:name
...
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(PRGM editor)
CTL
1:If
2:Then
3:Else
(PRGM editor)
I/O
1:Input
2:Prompt
3:Disp
(PRGM editor)
EXEC
1:name
2:name
...
4:For(
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHome
9:ClrTable
0:GetCalc(
A:Get(
5:While
6:Repeat
7:End
8:Pause
9:Lbl
0:Goto
A:IS>(
B:DS<(
B:Send(
C:Menu(
D:prgm
E:Return
F:Stop
G:DelVar
H:GraphStyle(
Tables and Reference Information A-43
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y [DRAW]
ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
DRAW
1:ClrDraw
2:Line(
POINTS
1:Pt-On(
STO
1:StorePic
2:RecallPic
3:StoreGDB
4:RecallGDB
2:Pt-Off(
3:Pt-Change(
4:Pxl-On(
5:Pxl-Off(
6:Pxl-Change(
7:pxl-Test(
3:Horizontal
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:DrawInv
9:Circle(
0:Text(
A:Pen
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
VARS
1:Window…
2:Zoom…
Y-VARS
1:Function…
2:Parametric…
3:Polar…
3:GDB…
4:Picture…
5:Statistics…
6:Table…
4:On/Off…
7:String…
VARS
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ
(Window…)
X/Y
(Window…)
T/q
(Window…)
U/V/W
1:u(nMin)
2:v(nMin)
3:w(nMin)
4:nMin
5:nMax
6:PlotStart
7:PlotStep
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
9:@Y
0:XFact
A:YFact
A-44 Tables and Reference Information
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VARS
ÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄ
(Zoom…)
ZX/ZY
(Zoom…)
ZT/Zq
(Zoom…)
ZU
1:Zu(nMin)
2:Zv(nMin)
3:Zw(nMin)
4:ZnMin
5:ZnMax
6:ZPlotStart
7:ZPlotStep
1:ZXmin
2:ZXmax
3:ZXscl
4:ZYmin
5:ZYmax
6:ZYscl
7:ZXres
1:ZTmin
2:ZTmax
3:ZTstep
4:Zqmin
5:Zqmax
6:Zqstep
VARS
ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ
(GDB…)
GRAPH DATABASE
1:GDB1
2:GDB2
...
(Picture…)
PICTURE
1:Pic1
2:Pic2
...
9:GDB9
0:GDB0
9:Pic9
0:Pic0
VARS
ÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄ
(Statistics…) (Statistics…) (Statistics…) (Statistics…) (Statistics…)
XY
1:n
2:v
G
EQ
1:RegEQ
2:a
3:b
4:c
5:d
6:e
TEST
1:p
2:z
PTS
1:Gx
2:Gx
3:Gy
4:Gy
1:x1
2:y1
3:x2
4:y2
5:x3
6:y3
7:Q1
8:Med
9:Q3
2
3:Sx
4:sx
5:w
6:Sy
7:sy
8:minX
9:maxX
0:minY
A:maxY
3:t
4:c2
2
5:Gxy
5:Û
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
Tables and Reference Information A-45
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VARS
ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(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…)
FUNCTION
1:Y1
(Parametric…)
PARAMETRIC
1:X1T
(Polar…)
POLAR
1:r1
(On/Off…)
ON/OFF
1:FnOn
2:Y2
2:Y1T
2:r2
2:FnOff
3:Y3
4:Y4
3:X2T
4:Y2T
3:r3
4:r4
...
9:Y9
...
A:X6T
5:r5
6:r6
0:Y0
B:Y6T
A-46 Tables and Reference Information
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y [DISTR]
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(
y [FINANCE]
ÚÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄ¿
CALC
VARS
1:Ú
2:æ
3:PV
4:PMT
5:FV
6:P/Y
7:C/Y
1:TVM Solver…
2:tvm_Pmt
3:tvm_æ
4:tvm_PV
5:tvm_Ú
6:tvm_FV
7:npv(
8:irr(
9:bal(
0:GPrn(
A:GInt(
B:4Nom(
C:4Eff(
D:dbd(
E:Pmt_End
F:Pmt_Bgn
Tables and Reference Information A-47
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y [MEM]
MEMORY
ÚÄÄÙ
ÚÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
MEMORY
1:Check RAM…
2:Delete…
3:Clear Entries
4:ClrAllLists
5:Reset…
(Check RAM…)
MEM FREE 27225
(Delete…)
DELETE FROM…
1:All…
2:Real…
3:Complex…
4:List…
5:Matrix…
6:Y-Vars…
7:Prgm…
(Reset…)
RESET
1:All Memory…
2:Defaults…
Real
Complex
List
15
0
0
0
Matrix
Y-Vars
Prgm
240
14
0
Pic
GDB
String
0
0
8:Pic…
9:GDB…
0:String…
MEMORY (Reset...)
y [CATALOG]
ÚÄÄÙ
ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(All Memory…)
RESET MEMORY
1:No
(Defaults…)
RESET DEFAULTS
1:No
CATALOG
cosh(
L1
cosh (
2:Reset
2:Reset
...
Equ4String(
expr(
...
inString(
...
Resetting memory
erases all data and
programs.
length(
...
sinh(
L1
sinh (
...
String4Equ(
sub(
...
tanh(
L1
tanh (
A-48 Tables and Reference Information
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Variables
User Variables
The TI.83 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 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.
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.
System Variables The variables below must be real numbers. You may store
to them. Since the TI.83 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.
The variables below are reserved for use by the TI.83. You
cannot store to them.
2
n, v, Sx, sx, minX, maxX, Gy, Gy , Gxy, a, b, c, RegEQ, x1, x2,
2
2
2
y1, z, t, F, c , Ç, v1, Sx1, n1, lower, upper, r , R and other
statistical variables.
Tables and Reference Information A-49
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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:
N
2
c
J =
− yi
∑
1+ ae −
bxi
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.
SinReg
The sine regression algorithm applies nonlinear recursive
least-squares techniques to optimize the following cost
function:
N
2
J =
a sin(bx +c) +d −y
i
[
]
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 recursively estimate the
constants a, b, c, and d to make J as small as possible.
A-50 Tables and Reference Information
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ANOVA(
The ANOVA Û statistic is:
Factor MS
Û =
Error MS
The mean squares (MS) that make up Û are:
Factor SS
Factor MS =
Factor df
Error SS
Error MS =
Error df
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:
Factor df = I −1 = numerator df for Û
I
Error df =
(ni −1) =denominator df for Û
∑
i=1
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
Tables and Reference Information A-51
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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
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.
A-52 Tables and Reference Information
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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
n2
+
+
n1
df =
2
2
2
2
1
Sx1
1
Sx2
n1 − 1 n1
n2 − 1 n2
otherwise:
2
(n1 −1)Sx12 +(n2 −1)Sx2
Sxp =
df
1
1
S =
+
Sxp
n1 n2
df =n1 +n2 −2
and Sxp is the pooled variance.
Tables and Reference Information A-53
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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:
− N
1 −(1 +i)
− N
0 = PV + PMT ×Gi
+ FV ×(1 +i)
i
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
ln
PMT ×Gi + PV ×i
ln(1 + i)
i ƒ 0
N =
where:
N =−(PV +FV) ÷PMT
where: i = 0
A-54 Tables and Reference Information
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−
i
PV + FV
(1+i)N −1
PMT =
× PV +
Gi
where:
i ƒ 0
PMT =−(PV +FV) ÷N
where:
i = 0
PMT × G
1
PMT × Gi
PV =
i − FV ×
−
i
(1+ i)N
i
where:
i ƒ 0
PV =−(FV +PMT ×N)
where:
i = 0
PMT × Gi
PMT × Gi
FV =
−(1+i)N × PV +
i
i
where:
i ƒ 0
FV =−(PV +PMT ×N)
where: i = 0
Tables and Reference Information A-55
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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)
Σ Int( ) =(pmt2 − pmt1+1) ×RND(PMT) −Σ Prn( )
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.
A-56 Tables and Reference Information
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Cash Flow
N
− nj
− Sj − 1 (1 −(1 +i)
)
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
Internal rate of return is dependent on the values of the
initial cash flow (CF0) and subsequent cash flows (CFj).
i = I% ÷ 100
4Eff( ) =100 ×(eCP ×ln(x +1) −1)
Interest Rate
Conversions
where:
x = .01 × NOM ÷ CP
4Nom( ) =100 ×CP × e1 ÷CP ×ln(x +1) −1
[
]
where:
x = .01 × EFF
EFF = effective rate
CP = compounding periods
NOM = nominal rate
Tables and Reference Information A-57
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Days between
Dates
With the dbd( function, you can enter or compute a date
within the range Jan. 1, 1950, through Dec. 31, 2049.
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
(Y2−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)
A-58 Tables and Reference Information
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General Information
B
Contents
Battery Information...................................... B-2
In Case of Difficulty ..................................... B-4
Error Conditions......................................... B-5
Accuracy Information.................................... B-10
Support and Service Information......................... B-12
Warranty Information.................................... B-13
General Information B-1
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Battery Information
When to Replace The TI.83 uses five batteries: four AAA alkaline batteries
the 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 displays this message when you turn on the unit.
After this message 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.
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 on page B.3, you can
replace either type of battery without losing any
information in memory.
Battery
Precautions
Take these precautions when replacing batteries.
•
•
•
•
•
•
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 batteries.
B-2 General Information
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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. Place your thumb on the
oval indentation on the battery cover. Push down and
toward you to slide the cover about ¼ inch (6 mm). Lift
off the cover to expose the battery compartment.
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 at the same
time. 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) diagrams in the
battery compartment.
•
To remove the lithium battery, place your index
finger on the battery. Insert the tip of a ball-point pen
(or similar instrument) under the battery at the small
opening provided in the battery compartment.
Carefully pry the battery upward, holding it with
your thumb and finger. (There is a spring that pushes
against the underside of the battery.)
•
Install the new battery, + side up, by inserting the
battery and gently snapping it in with your finger.
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 (step 1; page B.4).
General Information B-3
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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 pages B.5 through B.9 for details
about specific errors, if necessary.
3. 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, press y
[MEM] 2 to select 2:Delete, and then delete some items
from memory (Chapter 18).
4. If the busy indicator (dotted line) is displayed, a graph
or program has been paused; the TI.83 is waiting for
input. Press Í to continue or press É to break.
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 B.2 and
B.3.
B-4 General Information
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Error Conditions
When the TI.83 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
Possible Causes and Suggested Remedies
ARCHIVED VAR
A function or instruction is archived and therefore cannot
be executed or edited. Use the unarchive command to
unarchive the variable before using it.
ARGUMENT
BAD GUESS
A function or instruction does not have the correct number
of arguments. See Appendix A and the appropriate chapter.
¦
¦
¦
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
¦
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.
BREAK
You pressed the É key to break execution of a program,
to halt a DRAW instruction, or to stop evaluation of an
expression.
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 to 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 allows for
undefined values on a graph.
¦
You attempted a linear regression with a vertical line.
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Error Type
Possible Causes and Suggested Remedies
DOMAIN
¦
You specified an argument to a function or instruction
outside the valid range. This error is not returned during
graphing. The TI.83 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 Name
Error in Xmit
A variable you attempted to transmit cannot be transmitted
because a variable with that name already exists in the
receiving unit.
¦
The TI.83 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.
¦
¦
You attempted to transfer data (other than L1 through
L6) from a TI.83 to a TI.82.
You attempted to transfer L1 through L6 from a TI.83 to
a TI.82 without using 5:Lists to TI82 on the LINK SEND
menu.
ILLEGAL NEST
INCREMENT
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 allows
for undefined values on a graph.
¦
¦
The increment in a For( loop is 0.
INVALID
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. For example, you may have transferred UnN1 to
the TI.83 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.
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Error Type
Possible Causes and Suggested Remedies
INVALID (cont.)
¦
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.
INVALID DIM
You specified dimensions for an argument that are not
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.
ITERATIONS
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.
¦
¦
irr( has exceeded the maximum number of permitted
iterations.
When computing æ, the maximum number of iterations
was exceeded.
LABEL
The label in the Goto instruction is not defined with a Lbl
instruction in the program.
MEMORY
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.
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Error Type
Possible Causes and Suggested Remedies
MemoryFull
¦
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.
¦
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.
MODE
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.
NO SIGN CHNG
¦
¦
¦
The solve( function or the equation solver did not 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.
NONREAL ANS
OVERFLOW
In Real mode, the result of a calculation yielded a complex
result. This error is not returned during graphing. The TI.83
allows for undefined values on a graph.
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 allows for undefined
values on a graph.
RESERVED
You attempted to use a system variable inappropriately.
See Appendix A.
SINGULAR MAT
¦
A singular matrix (determinant = 0) is not valid as the
L1
argument for
.
¦
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
allows for undefined values on a graph.
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Error Type
Possible Causes and Suggested Remedies
SINGULARITY
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.
STAT
You attempted a stat calculation with lists that are not
appropriate.
¦
¦
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.
STAT PLOT
SYNTAX
You attempted to display a graph when a stat plot that uses
an undefined list is turned on.
The command contains a syntax error. Look for misplaced
functions, arguments, parentheses, or commas. See
Appendix A and the appropriate chapter.
TOL NOT MET
UNDEFINED
You requested a tolerance to which the algorithm cannot
return an accurate result.
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.
WINDOW RANGE
A problem exists with the window variables.
¦
¦
¦
¦
¦
You defined Xmax Xmin or Ymax Ymin.
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’s numerical range.
ZOOM
¦
¦
A point or a line, instead of a box, is defined in ZBox.
A ZOOM operation returned a math error.
General Information B-9
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Accuracy Information
Computational
Accuracy
To maximize accuracy, the TI.83 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.
Graphing
Accuracy
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.
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.
B-10 General Information
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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.
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| 230.25850929940
|x| < 10100
x
e
x
10
sinh x, cosh x
tanh x
sinhL1 x
|x| < 5 × 1099
1 x < 5 × 1099
L1 < x < 1
0 x < 10100
coshL1 x
tanhL1 x
‡x (real mode)
‡x (complex mode) |x| < 10100
x!
L.5 x 69, where x is a multiple of .5
Function Results
Function
sinL1 x, tanL1 x
cosL1 x
Range of Result
L90¡ to 90¡ or Lpà2 to pà2 (radians)
0¡ to 180¡ or 0 to p (radians)
General Information B-11
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Support and Service Information
Product Support
Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands
For general questions, contact Texas Instruments Customer Support:
phone: 1.800.TI.CARES (1.800.842.2737)
e-mail: ti-cares@ti.com
For technical questions, call the Programming Assistance Group of Customer
Support:
phone: 1.972.917.8324
Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands
Contact TI by e-mail or visit the TI calculator home page on the World Wide Web.
e-mail:
Internet:
ti-cares@ti.com
Product Service
Customers in the U.S. and Canada Only
Always contact Texas Instruments Customer Support before returning a product
for service.
Customers outside the U.S. and Canada
Refer to the leaflet enclosed with this product or contact your local Texas
Instruments retailer/distributor.
Other TI Products and Services
Visit the TI calculator home page on the World Wide Web.
Refer to the leaflet enclosed with this product or contact your local Texas
Instruments retailer/distributor.
B-12 General Information
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Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for 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.
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.
General Information B-13
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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.
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.
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 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 Customers Outside the U.S. and Canada
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.
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Index
+
(addition), 2-3, A-38
2
c cdf( (chi-square cdf), 13-31, A-3
computational and graphing, B-10
alpha cursor, 1-5
2
c pdf( (chi-square pdf), 13-31, A-4
2
c .Test (chi-square test), 13-22, A-4
:
+
3
(colon), 6, 16-5
(concatenation), 15-6, A-38
(cube), 2-6, A-35
3
‡( (cube root), 2-6, A-35
¡
à
=
(degrees notation), 2-3, A-34
(division), 2-3, A-37
(equal-to relational test), 2-25,
A-35
!
ì
í
ç
>
‚
(factorial), 2-21, A-34
(graph style, animate), 3-9
(graph style, dot), 3-9
(graph style, line), 3-9
(greater than), 2-25, A-35
(greater than or equal to), 2-25,
A-35
(inverse), 2-3, 8-9, 10-10, A-36
(less than), 2-25, A-35
(less than or equal to), 2-25, A-36
alpha key, 3
alpha-lock, 1-8
calculating schedules, 14-9
L1
<
angle modes, 1-11
{ } (list indicator), 11-4
[ ] (matrix indicator), 10-7
'
ä
M
(minutes notation), 2-23, A-38
(multiplication), 2-3, A-37
(negation), 1-23, 2-4, A-37
(not equal to), 2-25, A-35
ƒ
( ) (parentheses), 1-23
p
›
+
¦
(pi), 2-4
formula, A-51
(pixel mark), 8-15, 12-34
(pixel mark), 8-15, 12-34
(pixel mark), 8-15, 12-34
Ö (plot type, box), 12-33
Ò (plot type, histogram), 12-32
Õ (plot type, modified box), 12-32
Ô (plot type, normal probability),
12-33
M1
M1
M1
arctangent (tan (), 2-3
augment(, 10-14, 11-15, A-3
Automatic Power Down™ (APDé), 1-2
automatic regression equation, 12-22
automatic residual list (RESID), 12-22
axes format, sequence graphing, 6-8
axes, displaying (AxesOn, AxesOff),
3-14, A-3
^
(power), 2-3, A-36, A-37
10^( (power of ten), 2-4, A-37
x
‡
(root), 2-6, A-35
(seconds notation), 2-23, A-38
(square), 2-3, A-36
"
2
‡( (square root), 2-3, A-37
Store, 1-14, A-28
" " (string indicator), 15-3
(subtraction), 2-3, A-38
!
AxesOff, 3-14, A-3
AxesOn, 3-14, A-3
N
Index-1
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. B .
backing up calculator memory, 19-4,
19-10
bal( (amortization balance), 14-9, A-3
batteries, 1-2, B-2
below graph style (ê), 3-9
binomcdf(, 13-33, A-3
modes (a+bi, re^qi), 1-12, 2-16, A-3,
A-22
(C/Y), 14-4, 14-14
binompdf(, 13-33, A-3
Boolean logic, 2-26
box pixel mark (›), 8-15, 12-34
Boxplot plot type ( Ö), 12-33
busy indicator, 1-4
13.21
conj( (conjugate), 2-18, A-4
. C .
CALCULATE menu, 3-25
Calculate output option, 13-6, 13-8
cash flow
calculating, 14-8
formula, A-57
irr( (internal rate of return), 14-8,
A-13
conversion), 15-7, A-8
npv( (net present value), 14-8, A-17
CATALOG, 15-2
CBL 2/CBL System, 16-21, 19-3, A-10
CBR, 16-21, 19-3, A-10
Check RAM (memory screen), 18-2
2
chi-square cdf (c cdf(), 13-31, A-3
2
chi-square pdf (c pdf(), 13-31, A-4
chi-square test (c .Test), 13-22, A-4
Circle( (draw circle), 8-11, A-4
Clear Entries, 18-4, A-4
clearing
2
A-19
entries (Clear Entries), 18-4, A-4
all lists (ClrAllLists), 18-4, A-4
drawing (ClrDraw), 8-4, A-4
list (ClrList), 12-20, A-4
4Rect (to rectangular conversion),
2-19, A-22
conversion), 2-24, A-23
String4Equ( (string-to-equation
conversion), 15-8, A-29
CoordOff, 3-14, A-5
table (ClrTable), 16-20, A-4
ClrAllLists (clear all lists), 18-4, A-4
ClrDraw (clear drawing), 8-4, A-4
ClrHome (clear home screen), 16-20,
A-4
CoordOn, 3-14, A-5
ClrList (clear list), 12-20, A-4
ClrTable (clear table), 16-20, A-4
coefficients of determination (r , R ),
12-23
correlation coefficient (r), 12-23, 12-25
to 12-27
2
2
cos( (cosine), 2-3, A-5
M1
cos ( (arccosine), 2-3, A-5
colon separator (:), 6, 16-5
combinations (nCr), 2-21, A-16
cosh( (hyperbolic cosine), 15-10, A-5
Index-2
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. D (continued) .
. D (continued) .
M1
cosh ( (hyperbolic arccosine), 15-10,
A-5
10-13, 11-11, A-6
cosine (cos(), 2-3, A-5
cross pixel mark (+), 8-15, 12-34
cube (3), 2-6, A-35
11-11, A-6
Disp (display), 16-18, A-6
display contrast, 1-3
cube root (3‡(), 2-6, A-35
CubicReg (cubic regression), 12-26,
A-5
cubic regression (CubicReg), 12-26,
A-5
cumulative sum (cumSum(), 10-15,
11-12, A-5
cumSum( (cumulative sum), 10-15,
11-12, A-5
display cursors, 1-5
DISTR DRAW (distributions drawing
menu), 13-35
distribution functions
cursors, 1-5, 1-8
C/Y (compounding-periods-per-year
variable), 14-4, 14-14
2
. D .
Data input option, 13-6, 13-7
days between dates (dbd(), 14-13, A-5,
A-58
A-58
decimal mode (float or fixed), 1-10
decrement and skip (DS<(), 16-14, A-7
definite integral, 2-7, 3-28, 4-8, 5-6
Degree angle mode, 1-11, 2-23, A-6
degrees notation (¡), 2-3, A-34
DELETE FROM menu, 18-3
delete variable contents (DelVar),
16-15, A-6
geometpdf(, 13-34, A-11
normalcdf(, 13-30, A-17
tcdf(, 13-31, A-29
Shade_t(, 13-36, A-27
DelVar (delete variable contents),
16-15, A-6
DependAsk, 7-3, 7-5, A-6
DependAuto, 7-3, 7-5, A-6
derivative. See numerical derivative
det( (determinant), 10-12, A-6
determinant (det(), 10-12, A-6
DiagnosticOff, 12-23, A-6
DiagnosticOn, 12-23, A-6
DMS (degrees/minutes/seconds entry
notation), 2-23, A-38
4DMS (to degrees/minutes/seconds),
2-24, A-7
dot graph style (í), 3-9
dot pixel mark (¦), 8-15, 12-34
Dot (plotting mode), 1-11, A-7
DrawF (draw a function), 8-9, A-7
2
2
diagnostics display mode(r, r , R ),
12-23
differentiation, 2-8, 3-28, 4-8, 5-6
Index-3
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. D (continued) .
drawing on a graph
. E (continued) .
Equ4String( (equation-to-string
conversion), 15-7, A-8
area between curves, 17-11
circles (Circle(), 8-11
functions and inverses (DrawF,
DrawInv), 8-9
lines (Horizontal, Line(, Vertical),
8-6, 8-7
line segments (Line(), 8-5
pixels (Pxl.Change, Pxl.Off, Pxl.On,
pxl.Test), 8-16
points (Pt.Change, Pt.Off, Pt.On),
8-14
tangents (Tangent), 8-8
text (Text), 8-12
box plots, 17-2
cobweb attractors, 17-8
using Pen, 8-13
DrawInv (draw inverse), 8-9, A-7
DRAW menu, 8-3
mortgage payments 17.18
parametric equations: ferris wheel
problem, 17-12
piecewise functions, 17-4
Sierpinski triangle, 17-7
equations, 17-6
DRAW instructions, 8-3 N 8.16
Draw output option, 13-6 N 13.8
DRAW POINTS menu, 8-14
DRAW STO (draw store menu), 8-17
dr/dq operation on a graph, 5-6
DS<( (decrement and skip), 16-14, A-7
DuplicateName menu, 19-5
dx/dt operation on a graph, 3-28, 4-8
5-6
examples—Getting Started
box with lid 9 to 16
defining a, 9
finding calculated maximum, 16
setting the viewing window, 12
. E .
e (constant), 2-4
e^( (exponential), 2-4, A-7
å (exponent), 1-7, 1-10, A-7
edit keys table, 1-8
4Eff( (to effective interest rate), 14-12,
A-7
zooming in on the graph, 15
zooming in on the table, 11
drawing a tangent line, 8-2
financing a car, 14-2
Else, 16-10
End, 16-12, A-8
Eng (engineering notation mode), 1-10,
A-8
entry cursor, 1-5
graphing a circle, 3-2
ENTRY (last entry key), 1-16
EOSé (Equation Operating System),
1-22
eqn (equation variable), 2-8, 2-12
equal-to relational test (=), 2-25, A-35
Equation Operating System (EOSé),
1-22
mean height of a population, 13-2
path of a ball, 4-2
pendulum lengths and periods, 12-2
polar rose, 5-2
Equation Solver, 2-8
equations with multiple roots, 2-12
Index-4
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. E (continued) .
. F (continued) .
examples—Getting Started (continued)
quadratic formula
A-8
floating-decimal mode (Float), 1-10,
converting to a fraction, 7
displaying complex results, 8
entering a calculation, 6
roots of a, 7-2
sending variables, 19-2
solving a system of linear equations,
10-2
fMin( (function minimum), 2-6, A-9
FnOff (function off), 3-8, A-9
For(, 16-10, A-9
unit circle, 9-2
volume of a cylinder, 16-2
examples—miscellaneous
convergence, 6-12
format settings, 3-13, 6-8
daylight hours in Alaska, 12-28
calculating outstanding loan
balances, 14-10
amortization, A-56
ANOVA, A-51
predator-prey model, 6-13
exponential regression (ExpReg),
12-26, A-8
cash flow, A-57
days between dates, A-58
expr( (string-to-expression conversion),
15-7, A-8
ExpReg (exponential regression),
12-26, A-8
logistic regression, A-50
sine regression, A-50
time value of money, A-54
free-moving cursor, 3-17
frequency, 12-24
expression, 1-6
converting from string (expr(), 15-7,
A-8
turning on and off (ExprOn,
ExprOff), 3-14, A-8
ExprOff (expression off), 3-14, A-8
ExprOn (expression on), 3-14, A-8
A-10
accuracy, 3-17
. F .
‰f(x)dx operation on a graph, 3-28
factorial (!), 2-21, A-34
family of curves, 3-16
Ûcdf(, 13-32, A-8
Fill(, 10-13, A-8
FINANCE CALC menu, 14-5
FINANCE VARS menu, 14-14
financial functions
CALC (calculate menu), 3-25
defining and displaying, 3-3
defining in the Y= editor, 3-5
defining on the home screen, in a
program, 3-6
amortization schedules, 14-9
cash flows, 14-8
days between dates, 14-13
interest rate conversions, 14-12
payment method, 14-13
time value of money (TVM), 14-6
deselecting, 3-7
displaying, 3-3, 3-11, 3-15
evaluating, 3-6
family of curves, 3-16
format settings, 3-13
Index-5
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. F (continued) .
. G (continued) .
Function graphing (continued)
free-moving cursor, 3-17
graph styles, 3-9
graphing modes, 1-11
graph styles, 3-9
maximum of (fMax(), 2-6, A-9
minimum of (fMin(), 2-6, A-9
modes, 1-11, 3-4, A-10
moving the cursor to a value, 3-19
overlaying functions on a graph,
3-16
panning, 3-19
pausing or stopping a graph, 3-15
Quick Zoom, 3-19
A-12
GridOff, 3-14, A-11
selecting, 3-7, 3-8, A-9
shading, 3-10
Smart Graph, 3-15
GridOn, 3-14, A-11
tracing, 3-18
window variables, 3-11, 3-12
Y= editor, 3-5
viewing window, 3-11
@X and @Y window variables, 3-12
ZOOM menu, 3-20
. H .
Histogram plot type (Ò), 12-32
home screen, 1-4
ZOOM MEMORY menu, 3-23
function integral (fnInt(), 2-7, A-9
functions and instructions table, A-2 to
A-2
future value, 14-5, 14-7, 14-14
present value, 14-5, 14-7, 14-14
FV (future-value variable), 14-4, 14-14
Horiz (horizontal split-screen mode),
hyperbolic functions, 15-10
hypothesis tests, 13-10 N 13.15
i (complex number constant), 2-17
.G .
gcd( (greatest common divisor), 2-15,
A-10
identity(, 10-13, A-11
GDB (graph database), 8-19
geometcdf(, 13-34, A-10
geometpdf(, 13-34, A-10
Get( (get data from CBL 2/CBL or
CBR), 16-21, A-10
GetCalc( (get data from TI.83), 16-21,
A-10
getKey, 16-20, A-10
If, 16-9, A-11
If-Then, 16-9, A-11
If-Then-Else, 16-10, A-11
imag( (imaginary part), 2-18, A-11
imaginary part (imag(), 2-18, A-11
implied multiplication, 1-23
increment and skip (IS>(), 16-13, A-13
IndpntAsk, 7-3, A-12
IndpntAuto, 7-3, A-12
independent variable, 7-3, A-12
inferential stat editors, 13-6
Getting Started, 1 to 18. See also
examples, Getting Started
Goto, 16-13, A-10
Index-6
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. I (continued) .
inferential statistics. See also stat tests;
confidence intervals
keyboard
layout, 2, 3
alternative hypotheses, 13-7
bypassing editors, 13-8
math operations, 2-3
key-code diagram, 16-20
calculating test results (Calculate),
13-8
. L .
confidence interval calculations,
13-8, 13-16 N 13.21
11-16, A-13
data input or stats input, 13-7
entering argument values, 13-7
graphing test results (Draw), 13-8
input descriptions table, 13-26
pooled option, 13-8
labels
graph, 3-14, A-13
STAT TESTS menu, 13-9
test and interval output variables,
13-28
Input, 16-16, 16-17, A-12
insert cursor, 1-5
inString( (in string), 15-7, A-12
instruction, definition of, 1-7
int( (greatest integer), 2-14, 10-11,
A-12
GInt( (sum of interest), 14-9, A-12
integer part (iPart(), 2-14, 10-11, A-12
integral. See numerical integral
interest rate conversions
Lbl (label), 16-13, A-13
lcm( (least common multiple), 2-15,
least common multiple (lcm(), 2-15,
less than (<), 2-25, A-35
lines, drawing, 8-6, 8-7
calculating, 14-12
4Eff( (compute effective interest
rate), 14-12, A-7
formula, A-57
4Nom( (compute nominal interest
rate), 14-12, A-16
receiving items, 19-5
to a CBL 2/CBL System or CBR, 19-3
LINK RECEIVE menu, 19-5
LINK SEND menu, 19-4
LinReg(a+bx) (linear regression),
12-26, A-14
internal rate of return (irr(), 14-8, A-13
intersect operation on a graph, 3-27
inverse (L1), 2-3, 8-9, 10-10, A-36
inverse cumulative normal distribution
(invNorm(), 13-30, A-12
inverse trig functions, 2-3
invNorm( (inverse cumulative normal
distribution), 13-30, A-12
iPart( (integer part), 2-14, 10-11, A-12
irr( (internal rate of return), 14-8, A-13
IS>( (increment and skip), 16-13, A-13
LinReg(ax+b) (linear regression),
12-25, A-14
LinRegTTest (linear regression t test),
13-24, A-14
@List(, 11-12, A-14
LIST MATH menu, 11-17
List4matr( (lists-to-matrix conversion),
10-14, 11-15, A-14
LIST NAMES menu, 11-6
LIST OPS menu, 11-10
Index-7
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. L (continued) .
lists, 11-1 to 11-18
accessing an element, 11-5
attaching formulas, 11-7, 12-14
clearing all elements, 12-12, 12-20
copying, 11-5
Fill(, identity(, randM(, augment(,
Matr4list(, List4matr(, cumSum(),
10-12 to 10-16
relational operations, 10-11
row+(, †row(, †row+( ), 10-15
selecting, 10-3
creating, 11-3, 12-12
deleting from memory, 11-5, 18-3
detaching formulas, 11-8, 12-16
dimension, 11-4, 11-11
entering list names, 11-6, 12-11
indicator ({ }), 11-4
naming lists, 11-3
storing and displaying, 11-4
using in expressions, 11-9
using to graph a family of curves,
3-16, 11-5
viewing, 10-5
maximum of a function (fMax(), 2-6,
A-9
using to select data points from a
plot, 11-13
using with math functions, 11-9
using with math operations, 2-3
ln(, 2-4, A-14
LnReg (logarithmic regression), 12-26,
A-14
log(, 2-4, A-14
A-15
logic (Boolean) operators, 2-26
Logistic (regression), 12-27, A-15
logistic regression formula, A-50
memory
backing up, 19-10
checking available, 18-2
deleting items from, 18-3
. M .
MATH CPX (complex menu), 2-18
MATH menu, 2-5
MATH NUM (number menu), 2-13
math operations, keyboard, 2-3
MATH PRB (probability menu), 2-20
Matr4list( (matrix-to-list conversion),
10-14, 11-16, A-15
resetting defaults, 18-6
Menu( (define menu), 16-14, A-15
menus, 4, 1-19
matrices, 10-1 to 10.16
accessing elements, 10-8
copying, 10-8
defining (Menu(), 16-14, A-15
map, A-39
defined, 10-3
scrolling, 1-19
deleting from memory, 10-4
dimensions, 10-3, 10-12, 10-13
displaying a matrix, 10-8
displaying matrix elements, 10-4
editing matrix elements, 10-6
min( (minimum), 2-15, 11-17, A-16
minimum operation on a graph, 3-27
minimum of a function (fMin(), 2-6, A-9
minutes notation ('), 2-23, A-38
ModBoxplot plot type (Õ), 12-32
Index-8
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. M (continued) .
modified box plot type (Õ), 12-32
mode settings, 1-9
probability), 13-30, A-17
a+bi (complex rectangular), 1-12,
2-16, A-3
re^qi (complex polar), 1-12, 2-16,
A-22
Connected (plotting), 1-11, A-4
Degree (angle), 1-11, 2-24, A-6
Dot (plotting), 1-11, A-7
Eng (notation), 1-10, A-8
Fix (decimal), 1-10, A-8
Float (decimal), 1-10, A-8
Full (screen), 1-12, A-10
Func (graphing), 1-11, A-10
G.T (screen), 1-12, A-11
Horiz (screen), 1-12, A-11
Normal (notation), 1-10, A-16
Par/Param (graphing), 1-11, A-18
Pol/Polar (graphing), 1-11, A-19
Radian (angle), 1-11, 2-24, A-21
Real, 1-12, A-22
numerical integral, 2-7, 3-28
one-proportion z confidence interval
one-variable statistics (1.Var Stats),
12-25, A-31
or (Boolean) operator, 2-26, A-17
Sci (notation), 1-10, A-25
Seq (graphing), 1-11, A-26
Sequential (graphing order), 1-12,
A-26
modified box plot type (Õ), 12-32
multiple entries on a line, 1-6
multiplication (ä), 2-3, A-37
multiplicative inverse, 2-3
panning, 3-19
mode), 1-9, 1-11, A-18
parametric equations, 4-5
CALC (calculate operations on a
. N .
Ú (number of payment periods
variable), 14-4, 14-14
nCr (number of combinations), 2-21,
A-16
nDeriv( (numerical derivative), 2-7,
A-16
free-moving cursor, 4-7
graph format, 4-6
graph styles, 4-4
negation (M), 1-23, 2-4, A-37
4Nom( (to nominal interest rate), 14-12,
A-16
nonrecursive sequences, 6-5
normal distribution probability
(normalcdf(), 13-30, A-17
Normal notation mode, 1-10, A-16
normal probability plot type (Ô),
12-33
moving the cursor to a value, 4-8
selecting and deselecting, 4-5
setting parametric mode, 4-4
tracing, 4-7
window variables, 4-5
Y= editor, 4-4
zoom operations, 4-8
parentheses, 1-23
path (ë) graph style, 3-9
Index-9
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. P (continued) .
Pause, 16-12, A-18
pausing a graph, 3-15
Pen, 8-13
permutations (nPr), 2-21, A-17
phase plots, 6-13
Pi (p), 2-4
Pic (pictures), 8-17, 8-18
pictures (Pic), 8-17, 8-18
pixel, 8-16
pixels in Horiz/G.T modes, 8-16, 9-6
Plot1(, 12-34, A-18
pooled option, 13-6, 13-8
PRGM CTL (program control menu),
PRGM I/O (Input/Output menu), 16-16
PRGM NEW menu, 16-4
Plot2(, 12-34, A-18
Plot3(, 12-34, A-18
PlotsOff, 12-35, A-18
PlotsOn, 12-35, A-18
plotting modes, 1-11
plotting stat data, 12-31
PMT (payment amount variable), 14-4,
14-14
Pmt_Bgn (payment beginning
variable), 14-13, A-19
Pmt_End (payment end variable),
14-13, A-19
creating new, 16-4
defined, 16-4
deleting, 16-4
editing, 16-6
renaming, 16-7
poissoncdf(, 13-34, A-19
poissonpdf(, 13-33, A-19
Pol/Polar (polar graphing mode), 1-9,
1-11, A-19
polar equations, 5-4
polar form, complex numbers, 2-17
4Polar (to polar), 2-19, A-19
polar graphing
CALC (calculate operations on a
graph), 5-6
subroutines, 16-22
defining and displaying, 5-3
equations, 5-4
free-moving cursor, 5-6
graph format, 5-5
z confidence interval), 13-20,
1.PropZTest (one-proportion z test),
13-14, A-20
graph styles, 5-3
moving the cursor to a value, 5-6
selecting and deselecting, 5-4
mode (Pol/Polar), 1-9, 1-11, 5-3,
A-19
2.PropZInt (two-proportion
z confidence interval), 13-21,
A-20
2.PropZTest (two-proportion z test),
13-15, A-20
tracing, 5-6
window variables, 5-4
Y= editor, 5-3
ZOOM operations, 5-6
PolarGC (polar graphing coordinates),
3-13, A-19
P4Rx(, P4Ry( (polar-to-rectangular
conversions), 2-24, A-21
Pt.Change(, 8-15, A-20
Pt.Off(, 8-15, A-20
Pt.On(, 8-14, A-20
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. P (continued) .
. R (continued) .
PV (present value variable), 14-4,
14-14
12-22, 12-29
p-value, 13-28
regression model
PwrReg (power regression), 12-27,
A-20
automatic regression equation,
12-22
Pxl.Change(, 8-16, A-21
Pxl.Off(, 8-16, A-21
Pxl.On(, 8-16, A-21
diagnostics display mode, 12-23
models, 12-25
RESET menu, 18-5
pxl.Test(, 8-16, A-21
P/Y (number-of-payment-periods-per-
year variable), 14-4, 14-14
. Q .
QuadReg (quadratic regression),
12-25, A-21
QuartReg (quartic regression), 12-26
Quick Zoom, 3-19, A-21
root (x‡), 2-6, A-35
. R .
r (radian notation), 2-24, A-34
r (correlation coefficient), 12-23
2
2
12-23
…row(, 10-16, A-23
conversions), 2-24, A-23
Radian angle mode, 1-11, 2-24, A-21
radian notation (r), 2-24, A-34
rand (random number), 2-20, A-21
randBin( (random binomial), 2-22,
A-21
randInt( (random integer), 2-22, A-22
randM( (random matrix), 10-13, A-22
randNorm( (random Normal), 2-22,
A-22
. S .
13-23, A-24
random seed, 2-20, 2-22
RCL (recall), 1-15, 11-9
re^qi (polar complex mode), 1-12,
2-16, A-22
interval), 13-19, A-24
Real mode, 1-12, A-22
real( (real part), 2-18, A-22
RecallGDB, 8-20, A-22
interval), 13-18, A-25
2.SampZTest (two-sample z test),
13-12, A-25
RecallPic, 8-18, A-22
4Rect (to rectangular), 2-19, A-22
rectangular form, complex numbers,
2-17
Scatter plot type ("), 12-31
Sci (scientific notation mode), 1-10,
A-25
RectGC (rectangular graphing
coordinates), 3-13, A-22
recursive sequences, 6-6
ref( (row-echelon form), 10-15, A-22
scientific notation, 1-7,1.10
screen modes, 1-12
second cursor (2nd), 1-5
second key (2nd), 3
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. S (continued) .
. S (continued) .
seconds DMS notation ("), 2-23
Select(, 11-12, A-25
selecting
shade above (é) graph style, 3-9
Shade(, 8-9, A-26
ShadeÛ(, 13-36, A-27
data points from a plot, 11-13
functions from the home screen or a
program, 3-8
functions in the Y= editor, 3-7
items from menus, 4
stat plots from the Y= editor, 3-7
Send( (send to CBL 2/CBL or CBR),
16-21, A-26
shading graph areas, 3-10, 8-10
mode), 1-12, A-27
sending. See transmitting
Seq (sequence graphing mode), 1-11,
A-26
seq( (sequence), 11-12, A-26
sequence graphing
M1
axes format, 6-8
CALC (calculate menu), 6-10
defining and displaying, 6-3
evaluating, 6-10
A-27
A-28
free-moving cursor, 6-9
graph format, 6-8
Smart Graph, 3-15
graph styles, 6-4
moving the cursor to a value, 6-9
nonrecursive sequences, 6-5
phase plots, 6-13
recursive sequences, 6-6
setting sequence mode, 6-3
selecting and deselecting, 6-4
TI.83 versus TI.82 table, 6-15
tracing, 6-9
SortA( (sort ascending), 11-10, 12-20,
A-28
A-28
setting, 9-3, 9-6
web plots, 6-11
window variables, 6-7
Y= editor, 6-4
split-screen values, 8-12, 8-16, 9-6
square root (‡(), 2-3, A-37
STAT CALC menu, 12-24
stat list editor
ZOOM (zoom menu), 6-10
Sequential (graphing order mode),
1-12, A-26
service information, B-12
setting
display contrast, 1-3
graph styles, 3-9
attaching formulas to list names,
12-14
graph styles from a program, 3-10
modes, 1-9
modes from a program, 1-9
split-screen modes, 9-3
split-screen modes from a program,
9-6
clearing elements from lists, 12-12
creating list names, 12-12
detaching formulas from list names,
12-16
displaying, 12-10
edit-elements context, 12-18
tables from a program, 7-3
Index-12
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. S (continued) .
. S (continued) .
stat list editor (continued)
editing elements of formula-
generated lists, 12-16
statistical plotting, 12-31
editing list elements, 12-13
enter-names context, 12-19
entering list names, 12-11
formula-generated list names, 12-15
removing lists, 12-12
from a program, 12-37
Histogram, 12-32
ModBoxplot (modified box plot),
plot), 12-33
restoring list names L1–L6, 12-12,
12-21
switching contexts, 12-17
view-elements context, 12-18
view-names context, 12-19
STAT PLOTS menu, 12-34
stat tests and confidence intervals
ANOVA( (one-way analysis of
variance), 13-25
tracing, 12-36
turning on/off stat plots, 3-7, 12-35
viewing window, 12-36
xyLine, 12-31
statistical variables table, 12-29
A-28
²
c .Test (chi-square test), 13-22
LinRegTTest (linear regression
t test), 13-24
1.PropZInt (one-proportion
z confidence interval), 13-20
1.PropZTest (one-proportion z test),
13-14
Store (!), 1-14, A-28
StorePic, 8-17, A-29
storing
graph databases (GDBs), 8-19
graph pictures, 8-17
2.PropZInt (two-proportion
z confidence interval), 13-21
2.PropZTest (two-proportion z test),
13-15
variable values, 1-14
conversions), 15-8, A-29
2.SampÛTest (two-sample Û.Test),
13-23
2.SampTInt (two-sample
t confidence interval), 13-19
2.SampTTest (two-sample t test),
13-13
2.SampZInt (two-sample
z confidence interval), 13-18
2.SampZTest (two-sample z test),
13-12
concatenation (+), 15-6, A-38
converting, 15-7, 15-8
defined, 15-3
displaying contents, 15-5
entering, 15-3
storing, 15-5
variables, 15-4
TInterval (one-sample t confidence
interval), 13-17
T.Test (one-sample t test), 13-11
ZInterval (one-sample z confidence
interval), 13-16
student-t distribution
probability (tcdf(), 13-31, A-29
probability density function (tpdf(),
13-30, A-30
sub( (substring), 15-9, A-29
subroutines, 16-15, 16-22
subtraction (N), 2-3, A-38
sum( (summation), 11-18, A-29
system variables, A-49
Z.Test (one-sample z test), 13-10
Stats input option, 13-6, 13-7
STAT TESTS menu, 13-9
statistical distribution functions. See
distribution functions
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. T .
TABLE SETUP screen, 7-3
tables, 7-1 to 7-6
Ú variable (number of payment
description, 7-5
variables, 7-3 to 7-5
tan( (tangent), 2-3, A-29
tan ( (arctangent), 2-3, A-29
tangent (tan(), 2-3, A-29
Tangent( (draw line), 8-8, A-29
tangent lines, drawing, 8-8
14-14
M1
periods per year), 14-14
tvm_I% (interest rate), 14-7, A-31
tanh( (hyperbolic tangent), 15-10, A-29
M1
tanh ( (hyperbolic arctangent), 15-10,
A-29
@Tbl (table step variable), 7-3
TblStart (table start variable), 7-3
tcdf( (student-t distribution
probability), 13-31, A-29
technical support, B-12
TEST (relational menu), 2-25
TEST LOGIC (Boolean menu), 2-26
Text(
TInterval (one-sample t confidence
interval), 13-17, A-30
density function), 13-30, A-30
TRACE
instruction, 8-12, 9-6, A-29
placing on a graph, 8-12
Then, 16-9, A-11
cursor, 3-18
thick (è) graph style, 3-9
TI.82
entering numbers during, 3-19, 4-8,
link differences, 19-9
transmitting to/from, 19-4, 19-8,
19-9
expression display, 3-14, 3-18
Trace instruction in a program, 3-19,
TI.83
transmitting
features, 17, 18
error conditions, 19-6
keyboard, 2, 3
key code diagram, 16-20
Link. See linking
from a TI.82 to a TI.83, 19-9
stopping, 19-6
menu map, A-39
TI.GRAPH LINK, 19-3
Time axes format, 6-8, A-30
time value of money (TVM)
calculating, 14-6
to an additional TI.83, 19-7
T (transpose matrix), 10-12, A-34
transpose matrix (T), 10-12, A-34
trigonometric functions, 2-3
T.Test (one-sample t test), 13-11, A-30
C/Y variable (number of
compounding periods per year),
14-14
formulas, A-54
FV variable (future value), 14-14
æ variable (annual interest rate),
14-14
Index-14
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. T (continued) .
turning on and off
. V (continued) .
axes, 3-14
calculator, 1-2
coordinates, 3-14
expressions, 3-14
functions, 3-7
grid, 3-14
labels, 3-14
graph pictures, 1-13
list, 1-13, 11-3
pixels, 8-16
points, 8-14
real, 1-13
stat plots, 3-7, 12-35
tvm_FV (future value), 14-7, A-31
tvm_I% (interest rate), 14-7, A-31
tvm_Ú (# payment periods), 14-7, A-31
tvm_Pmt (payment amount), 14-6,
A-31
recalling values, 1-15
string, 15-4, 15-5
types, 1-13
tvm_PV (present value), 14-7, A-31
two-proportion z confidence interval
(2.PropZInt), 13-21, A-20
two-proportion z test (2.PropZTest),
13-15, A-20
two-sample Û-Test formula, A-52
two-sample t test formula, A-53
two-variable statistics (2.Var Stats),
12-25, A-31
user and system, 1-13, A-49
A-31
A-31
VARS menu
Picture, 1-21
String, 1-21
. U .
u sequence function, 6-3
user variables, A-49
uv/uvAxes (axes format), 6-8, A-31
uw/uwAxes (axes format), 6-8, A-31
Zoom, 1-21
Vertical (draw line), 8-6, A-31
viewing window, 3-11
vw/uvAxes (axes format), 6-8
. V .
v sequence function, 6-3
1.Var Stats (one-variable statistics),
12-25, A-31
2.Var Stats (two-variable statistics),
12-25, A-31
. W .
w sequence function, 6-3
warranty information, B-13
Web (axes format), 6-8, A-31
web plots, sequence graphing, 6-11
While, 16-11, A-32
value operation on a graph, 3-25
window variables
function graphing, 3-11
parametric graphing, 4-5
polar graphing, 5-4
sequence graphing, 6-7
Index-15
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. X .
XFact zoom factor, 3-24
x-intercept of a root, 3-26
xor (Boolean) exclusive or operator,
2-26, A-32
ZoomSto (store zoom window), 3-23,
ZPrevious (use previous window),
ZStandard (use standard window),
3-22, A-33
xth root (x‡), 2-6
xyLine (Ó) plot type, 12-31
@X window variable, 3-12
A-34
. Y .
YFact zoom factor, 3-24
Y= editor
function graphing, 3-5
parametric graphing, 4-4
polar graphing, 5-3
sequence graphing, 6-4
Y.VARS menu
Function, 1-21
Parametric, 1-21
Polar, 1-21
On/Off, 1-21
@Y window variable, 3-12
. Z .
ZBox, 3-20, A-32
ZDecimal, 3-21, A-32
zero operation on a graph, 3-26
ZInteger, 3-22, A-32
ZInterval (one-sample z confidence
interval), 13-16, A-32
zoom, 3-20 to 3-24
cursor, 3-20
factors, 3-24
function graphing, 3-20
parametric graphing, 4-8
polar graphing, 5-6
sequence graphing, 6-10
ZoomFit (zoom to fit function), 3-22,
A-33
Zoom In (zoom in), 3-21, A-32
ZOOM menu, 3-20
ZOOM MEMORY menu, 3-23
Zoom Out (zoom out), 3-21, A-32
ZoomRcl (recall stored window), 3-23,
A-33
ZoomStat (statistics zoom), 3-22, A-33
Index-16
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Download from Www.Somanuals.com. All Manuals Search And Download.
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