Texas Instruments Calculator TI 36X User Manual

TI-36X  
ý
Scientific Calculator  
USER’S GUIDE  
2000, 2003 Texas Instruments Incorporated  
education.ti.com  
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Turning the Calculator On and Off  
The TI-36X  
ü
is battery powered.  
To turn on the TI  
-
36X  
ü
, press  
T.  
To turn off the TI  
memory is retained.  
-
36X  
ü, press %r. All data in  
APD  
é
TI-36X  
(Automatic Power Downé) turns off the  
ü
automatically if no key is pressed for about  
five minutes. Press after APD to power up again;  
T
the display, pending operations, settings, and memory  
are retained.  
Alternate Functions  
Most keys can perform two functions. The first function  
is marked on the key, and the second function is  
marked above the key, as illustrated below.  
ì
2nd function  
Primary function  
P
Press  
%
to activate the second function of a key. To  
cancel the second function before making an entry,  
press again. In this manual, second functions are  
%
shown in brackets ([ ]). For example, press  
P
to find  
the square of a number. Press %n to find the  
square root of a number.  
1
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Display  
The TI-36X  
ü
has a two-line display. The first line  
(Entry Line) displays an entry of up to 88 digits or  
items (47 for Stat or Stored Operations). Entries begin  
on the left; those with more than 11 digits scroll to the  
left. You can have as many as 23 levels of parentheses  
and up to 8 mathematical operations pending.  
The second line (Result Line) displays a result of up to  
10 digits, plus a decimal point, a negative sign, a x10  
indicator, and a 2-digit positive or negative exponent.  
Results that exceed the digit limit are displayed in  
scientific notation.  
Note: In the text, numbers containing decimal fractions  
are shown in decimal format consistent with the  
calculator display.  
Scrolling  
Scroll with  
"
,
!
,
#
, and  
$.  
Press  
"
and  
!
to scroll horizontally through the  
current or previous entries, or to move the  
underscore within a menu list. Press %" or  
%! to move the cursor to the beginning or end  
of the entry.  
After an expression is evaluated, press  
to scroll through previous entries, which are stored  
in the TI-36X history. If you edit a previous entry  
and press , the calculator will evaluate the  
new expression and return the new result.  
#
and  
$
ü
V
2
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Menus  
Some key presses access menus:  
S
,
R,  
e
,
-
,
8
,
&
,
/
,
,
.
%m  
,
%q  
,
%p  
%]  
%Z  
,
%d  
%6  
%t  
,
%^  
,
,
,
%f  
,
%h  
,
,
,
%\, and %s  
.
The menu choices are displayed on the screen. Press  
"
or to scroll through the menu and underline an  
!
item. To select an underlined item:  
Press  
V
while the item is underlined. Or,  
For menu items followed by an argument value,  
enter the argument value while the item is  
underlined. The item and the argument value are  
transferred to the current entry. However, if the  
argument is another function, you need to press  
V
to the next.  
to select the first function before proceeding  
To return to the previous screen without selecting the  
menu item, press  
4.  
Fix  
%t displays a menu: F0123456789. To round  
displayed results, scroll with or to select the  
"
!
desired number of decimal places, or enter the numeral  
corresponding to the desired number of decimal places.  
The displayed value is padded with zeroes if needed.  
To restore standard notation (floating decimal), select F  
(default) in the menu, or press %tI  
.
You can specify rounding places before you begin your  
calculations, before you complete an operation with  
V
, or after the results are displayed.  
3
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Clearing, Correcting, and Resetting  
Key  
Action  
4
Action depends on position of the cursor.  
If cursor is in the middle of an entry,  
clears character under the cursor and  
all characters to the right of the  
cursor.  
If cursor is at the end of an entry,  
clears the entire entry.  
If an Error message is displayed,  
clears the error message and moves  
the cursor to last entry in history.  
If a menu is displayed, exits menu.  
'
If the cursor is on a character, deletes  
the character under the cursor.  
If the cursor is at the end of an entry,  
deletes the character to the left of the  
cursor.  
%[  
Lets you insert one or more characters at  
the cursor.  
%s Resets the TI-36X  
ü. Returns unit to  
"V  
default settings; clears memory variables,  
pending operations, all entries in history,  
statistical data, Ans, and stored  
or  
T
&4  
(simul-  
operations. MEM CLEARED is displayed.  
taneously)  
You can overwrite entries. Move the cursor to the  
desired location and begin pressing keys. The new  
keypresses will overwrite the existing entry, character  
by character.  
Before beginning a new set of examples or problems in  
this manual, reset the calculator to ensure that your  
displays will be the same as those shown.  
4
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Display Indicators  
Special indicators may appear in the display to provide  
additional information about functions or results.  
Indicator  
2nd  
Meaning  
2nd function is active.  
FIX  
Calculator is rounding results to  
specified number of places.  
SCI or ENG  
Scientific or engineering notation is  
active.  
STAT  
Calculator is in Statistics mode.  
DEG, RAD,  
or GRAD  
Specifies angle-unit setting (degrees,  
radians, or grads). The default is the  
degree setting.  
HEX or OCT Calculator is in hexadecimal or octal  
mode.  
x10  
Precedes the exponent in scientific or  
engineering notation.  
# $  
An entry is stored in memory before  
and/or after the active screen. Press  
#
and  
An entry or menu list extends beyond  
the capacity of the screen. Press and  
to scroll.  
$
to scroll.  
" !  
"
!
r or i  
Complex number, real part, or  
complex number, imaginary part.  
µ
Calculator is busy.  
5
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Order of Operations  
The TI-36X  
ü
uses EOS  
è
(Equation Operating  
System) to evaluate expressions.  
Order Evaluation  
1st  
Expressions inside parentheses.  
2nd  
Functions which need a ) and precede the  
argument, such as sin, log, and all R  
/P  
menu items; Boolean Logic NOT and 2s  
complement.  
3rd  
4th  
Fractions.  
Functions that are entered after the argument,  
such as x2 and angle unit modifiers (é ê ë r g);  
metric conversions.  
5th  
Exponentiation (^) and roots (x  
).  
6th  
Negation (L).  
7th  
Permutations (nPr) and combinations (nCr).  
Multiplication, implied multiplication, division.  
Addition and subtraction.  
8th  
9th  
10th  
11th  
12th  
13th  
Boolean logic AND.  
Boolean logic XOR and OR.  
d
Conversions (  
4
Ab/c  
/
/e,  
4F  
/
D, 4DMS).  
V
open parentheses.  
completes all operations and closes all  
You can change the order of operations by enclosing  
expressions in parentheses.  
6
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Basic Operations  
As you press keys, numerals, operators, and results  
appear on the display.  
H
C
,
,
?
D
,
,
@
E
,
,
A
F
,
,
B
G
,
Enters numerals 0 through 9.  
:
,
;
,
<
,
=
Adds, subtracts, multiplies,  
divides.  
N
,
O
Opens, closes a parenthetical  
expression.  
I
Inserts the decimal point.  
Enters a negative sign.  
Completes all operations.  
J
V
Last Answer  
%u recalls the value of the most recently  
calculated result and enters it into the current entry as  
Ans.  
If you press an operator key immediately after  
completing an operation with  
V, the most recently  
calculated result is recalled and entered as Ans.  
7
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³
Examples  
ß
5
è
è
9+6-2  
5 < 9 : 6 ; 2 V  
49.  
ß
5
(9+6)-2  
5 < N 9 : 6 O ; 2 V  
W 8 8 7 <  
73.  
ß
Ansñ8.7  
8.390804598  
F0123456789  
% t " " " "  
V
ß
Ansñ8.7  
8.391  
ß
5
è
è
2+Ans  
5 < 2 : % u % t 6  
V
18.390805  
5
29  
% t I  
ß
2+Ans  
18.3908046  
5
è
è
(9+6)-2  
(8+6)-2  
ø
# # #  
ß
5
" " " ' % [ 8 V  
% s " V  
68.  
MEM CLEARED  
8
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Percent  
To calculate a percent, press %l after entering a  
value.  
³
Problem  
A mining company mines 5000 tons of ore having a  
3-percent concentration of metal, 7300 tons having a  
2.3-percent concentration, and 8400 tons having a  
3.1-percent concentration. How much metal does the  
company get in total from the three quantities of ore?  
If the metal is worth $280 per ton, what is the value of  
the total amount of metal present in the three quantities  
of ore?  
ß
5000è3%  
5 0 0 0 < 3 % l V  
150.  
Ans+7300  
è
2. Þß  
: 7 3 0 0 < 2 I 3 % l  
V
317.9  
Ans+8400  
è
3. Þß  
: 8 4 0 0 < 3 I 1 % l  
V
578.3  
ß
Ansè  
280  
< 2 8 0 V  
161924.  
The three quantities of ore together contain 578.3 tons  
of metal. The value of the metal is $161924.  
9
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Fractions  
Fractional calculations can display fractional or decimal  
results. Results are automatically simplified.  
1
Enters a fraction. Press  
1
after  
entering whole number, and between  
numerator and denominator, both of  
which must be positive integers. To  
negate a fraction or a mixed number,  
press  
J
argument.  
before entering the first  
%` Converts from mixed number to simple  
fraction, and vice versa.  
%_  
Converts from fraction to decimal format  
and vice versa. Note: Due to display  
size, not all decimal numbers can be  
converted to fractions.  
If a problem contains both fractions and decimals, the  
results will be displayed in decimal format.  
³
Examples  
4ç  
3ç  
5+2  
6
ç
ð
1
4
ç
ñ
5ß  
5
4 1 3 1 5 : 2 1 1 1  
5 V  
d
ß
Ans  
4
Ab/c34  
F34D  
/
c
% ` V  
34  
ñ
5
ß
Ans  
4
% _ V  
6.8  
ß
AnsèM  
3ç  
10  
< J 3 1 1 0 V  
M
2.04  
10  
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Exponents, Roots, and Reciprocals  
P
K
Calculates the square of a value.  
Raises a value to any power within the range  
of the calculator. If the number is negative,  
the power must be an integer. If you include  
an operation in the exponent, you must use  
parentheses.  
%n Calculates the square root of a positive  
value.  
%j Calculates any root of any positive value  
(within the range of the calculator) and any  
odd-numbered integer root of a negative  
value.  
%k Yields the reciprocal of a value.  
³
Examples  
ß
52+4^(2+1)  
5 P : 4 K N 2 : 1 O V  
89.  
ß
ì
(49)  
% n 4 9 O V  
7.  
ß
6xì64  
6 % j 6 4 V  
2.  
ß
25-1  
2 5 % k V  
0.04  
11  
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Notation  
%Z displays the Numeric Notation mode  
menu.  
FLO (default): Displays results in floating notation,  
with digits to the left and right of the decimal point.  
SCI: Displays results in scientific notation. The  
format of scientific notation is n x 10^p, where  
1{n<10 and p is an integer.  
ENG: Engineering notation (exponent is a multiple  
of 3).  
These modes affect only the display of results, and not  
the internally stored results.  
M
lets you enter a value in scientific notation,  
regardless of the numeric notation mode. Press  
before entering a negative exponent.  
J
³
Examples  
ß
1.2E5+4.6E7  
1 I 2 M 5 + 4 I 6 M 7 V  
46120000.  
ß
1.2E5+4.6E7  
% Z " V  
% Z " V  
4.612X1007  
ß
1.2E5+4.6E7  
46.12X1006  
12  
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Pi  
5
enters the value of p. It is stored internally to 13  
digits (3.141592653590) and displayed to 10 digits  
(3.141592654).  
When multiplying  
p
by a number, you do not need to  
press  
<; multiplication is implicit.  
³
Examples  
Find the circumference and the area of a circle having a  
radius of 5 centimeters. Find the surface area of a  
sphere having a radius of 5 centimeters. (Remember:  
circumference=2  
p
r; area =  
p
r 2; surface area=(4  
p
)r 2.)  
Use the Fix function to display results rounded to the  
nearest whole number.  
ß
2pè5  
% t " V 2 5 < 5  
V
31.  
ß
pè52  
# ' " " " P V  
79.  
ß
4
pè52  
# % [ 4 V  
314.  
The circumference of the circle is 31 centimeters, and  
the area is 79 square centimeters. The surface area of  
the sphere is 314 square centimeters.  
13  
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Memory  
The TI  
-
36X  
ü
has five memory variables. You can  
store a real number or an expression that results in a  
real number to a memory variable. For storing complex  
numbers to memory, see page 31.  
S
Lets you store values to variables.  
Recalls the values of variables.  
%q  
R
Recalls variables by letter designation.  
%p Displays menu: CLR VAR: Y N.  
Select Y (yes) and press  
V
to clear  
all memory variables and re-initialize  
seed in E.  
When you press  
A, B, C, D, and E. Press  
Press , and the value of your last answer is  
S
, a menu of variables displays:  
"
or to select a variable.  
!
V
stored into the variable you have selected. If that  
variable already contains a value, the new one will  
replace it.  
If you enter an expression and press  
S
and then  
V
, the TI-36X will simultaneously evaluate the  
ü
expression and store the resulting value to the memory  
variable you select.  
Press %q to display the menu of memory  
variables. Press  
"
or  
!
to select the variable you wish  
. The value in this variable is  
to recall and press  
V
inserted into your current entry at the cursor.  
Pressing also displays the menu of memory  
R
variables, and you select the one you wish to recall.  
However, the variable name rather than the value itself  
is inserted into your current entry. Since the variable  
name contains the value, evaluation of the expression  
yields the same results.  
14  
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In addition to serving as a memory variable, E stores a  
seed value to generate a random number when you are  
using the Probability function (see page 32).  
³
Problem  
A gravel quarry is opening two new pits: one is 350  
meters by 560 meters, and the other is 340 meters by  
610 meters. What volume of gravel would the company  
remove from each if they excavated to a depth of 150  
meters? To a depth of 210 meters? Display results in  
engineering notation.  
ß
350è  
560"A  
% Z " " V 3 5 0 <  
5 6 0 S V  
196.x1003  
ß
340  
150  
210  
150  
210  
è610"B  
3 4 0 < 6 1 0 S " V  
1 5 0 < % q V V  
2 1 0 < % q V V  
1 5 0 < R " V V  
2 1 0 < R " V V  
207.4x1003  
ß
è
è
è
è
196000  
29.4x1006  
ß
196000  
41.16x1006  
ß
B
31.11x1006  
ß
B
43.554x1006  
From the first pit: 29.4 million cu.m. and 41.16 million  
cu.m., respectively. From the second pit: 31.11 million  
cu.m. and 43.554 million cu.m., respectively.  
15  
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Stored Operations  
The TI-36X  
ü
stores two operations, Op1 and Op2. To  
store an operation to Op1 or Op2 and recall it:  
1. Press %b or %c  
2. Enter the operation, beginning with an operator  
(such as +, , or ^). You can store any  
.
M
,
Q,  
P
combination of numbers, operators, and menu items  
and their arguments, to a limit of 47 characters or  
items.  
3. Press  
4. Each subsequent time you press  
TI-36X recalls the stored operation and applies it  
V
to save the operation to memory.  
2
or 3, the  
ü
to the last answer. The expression with the stored  
operation appears on the first line of the display,  
and the result appears on the second line. A  
counter on the left side of the result line displays the  
number of consecutive times you have pressed Op1  
or Op2.  
You can set the TI-36X  
ü
to display only the counter  
and the result, and not the expression on the entry line.  
Press %b or %c, press  
!
until the = is  
highlighted (  
û
) and press  
V
. Repeat to toggle this  
setting off.  
16  
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³
Examples  
OP1=  
è
2
% b < 2 V  
ß
3è2  
3 2  
1
6.  
ß
6è  
2
2
2
12.  
ß
12è  
2
2
3
24.  
OP2=+5  
% c : 5 V  
ß
10+5  
1
1 0 3  
3
15.  
ß
15+5  
2
20.  
ß
20+5  
3
3
25.  
ß
25è2  
2
1
50.  
ß
50+5  
1
3
55.  
17  
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Logarithms  
%d displays a menu of log functions.  
log  
10^  
ln  
Yields the common logarithm of a number.  
Raises 10 to the power you specify.  
Yields the logarithm of a number to the base e  
(e=2.718281828495).  
e^  
Raises e to the power you specify.  
Select the function on the menu, then enter the value  
and complete the expression with  
O.  
³
Examples  
Þ
log 10^  
% d  
ß
log(100)  
1 0 0 O V  
2.  
ß
10^(3.2)  
% d " 3 I 2 O V  
1584.893192  
ß
ln(9.453)  
% d " " 9 I 4 5 3 O  
V
2.246332151  
ß
e^(4.7)  
% d ! 4 I 7 O V  
109.9471725  
18  
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³
Problem  
A radioactive substance decays exponentially. If y  
grams of certain radioactive substance are initiallyo  
present, the number of grams y(t) after t days is given  
by the formula:  
y(t)=yoe-0.00015t  
After 340 days, how much of a 5-gram sample of this  
radioactive substance remains? After 475 days? Store  
the constant part of the exponent to memory so you  
need enter it only once. Round results to two decimal  
places.  
ß
L
0.00015ÞA  
J 0 I 0 0 0 1 5 S V  
L
0.00015  
ß
5èe^(Aè340)  
5 < % d " " " V  
R < 3 4 0 O V  
4.751393353  
ß
5è  
e^(Aè  
340)  
% t 2  
4.75  
ß
5è  
e^(Aè  
475)  
5 < % d " " " V  
R < 4 7 5 O V  
4.66  
About 4.75 grams of this radioactive substance remain  
after 340 days, and 4.66 grams remain after 475 days.  
19  
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Trigonometric Functions  
e
displays a menu of the trigonometric functions  
(sin, sin-1, cos, cos-1, tan, tan-1). Press  
"
or  
!
to  
select the desired function, enter the value, and close  
the parentheses with  
O.  
Set the desired angle mode before starting  
trigonometric calculations. The problems below assume  
the default, which is degree mode. See the section on  
Angle Modes (page 22) for other angle modes.  
³
Examples  
Ýcos cos-1  
Þ
e " "  
ß
cos(30)  
3 0 O % t 4 V  
e "  
0.8660  
Þ
sin sin-1  
sin-1(0.7391  
Þß  
0 I 7 3 9 1 O V  
47.6548  
cos(tan-1(1)  
Þß  
e " " V e ! 1 O  
O V  
0.7071  
20  
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³
Problem  
Find angle a in the right triangle below. Then find the  
length of the hypotenuse h and angle b. Measurements  
of length and height are in meters. Round off results to  
one decimal place.  
h
b
3
a
7
Remember 3/7=tan a, so a=tanL1(3/7). Then 3/h=sin a,  
so h=3/sin a. Then 7/h=sin b, so b=sinL1(7/h).  
ß
tan-1(3  
ñ7)  
% t 1 e ! 3 = 7 O  
V
23.2  
ß
sin(Ans)  
e % u O V  
3 = % u V  
0.4  
ß
3ñAns  
7.6  
ß
sin-1(7  
ñAns)  
e " 7 = % u O V  
66.8  
Angle a is about 23.2 degrees. The hypotenuse h is  
about 7.6 meters. Angle b is about 66.8 degrees.  
21  
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Angle Modes  
/
displays a menu to specify the angle unit modifier  
for an entry: degrees (  
é
), radians (r), grads (g), or DMS  
(
é ê ë). It also lets you convert an angle to DMS  
Notation (4DMS).  
You can use a DMS value in calculations, but then the  
results will no longer be in DMS format; the calculator  
will automatically convert to decimal format.  
³
Problem  
Two adjacent angles measure 12é31ê45ë and  
26é54ê38ë, respectively. Sum the two angles and  
display the results in DMS format.  
Þ
é ê ë  
r
g
1 2 /  
12é  
12é  
12é  
31  
31  
31  
3 1  
ê
46  
ë
ë
+
/ " 4 6 / " " :  
ê46  
+2Þß  
2 6 / 5 4 / " 3 8 / " "  
V V  
39.44  
ß
Ans4DMS  
/ ! V V  
39 26  
é
ê24ë  
22  
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&
displays a menu (DEG RAD GRD) to express  
angle measurements in degrees (default), radians, or  
grads, respectively.  
³
Problem  
/6 radians. In the default  
. Then set the  
You probably know that 30  
é=å  
Degree Mode, find the sine of 30  
é
calculator to Radian Mode and find the sine of  
å/6  
radians.  
ß
sin(30)  
e 3 0 O V  
0.5  
ß
sin(åñ6)  
& " V " 5 = 6 O  
V
0.5  
You can override the Angle Mode with the  
/
key.  
Keep the calculator in Radian Mode and find the sine of  
30 . Then return the calculator to Degree Mode and  
find the sine of /6 radians.  
é
å
ß
sin(30  
é
)
e 3 0 / O V  
0.5  
ß
sin((åñ6)r  
)
& ! V " N 5 = 6 O  
/ " " " O V  
0.5  
23  
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Rectangular  
/Polar  
%^ displays a menu to convert rectangular  
coordinates (x, y) to polar coordinates (r, ) or vice  
æ
versa. For each coordinate to which you are converting,  
enter both values expressed in the format from which  
you are converting, separated by a comma, then close  
the parentheses with  
O
before you complete the  
operation with  
V. Set angle mode, as necessary,  
before starting calculations.  
³
Examples  
Convert polar coordinates (r,  
æ)=(5, 30) into rectangular  
coordinates. Then convert rectangular coordinates  
(x, y)=(3, 4) into polar coordinates. Round all results to  
1 decimal place.  
ß
P4Rx(5,30)  
% ^ " " 5 % i 3 0 O  
% t " " V V  
4.3  
ß
P4Ry(5,30)  
% ^ " " " 5 % i 3 0  
O V  
2.5  
ß
R4Pr(3,4)  
% ^ 3 % i 4 O V  
5.0  
ß
R4Pq(3,4)  
% ^ " 3 % i 4 O  
V
53.1  
(r,  
q
)=(5, 30) converts to (x, y)=(4.3, 2.5). (x, y) = (3, 4)  
converts to (r,  
q)=(5.0, 53.1).  
24  
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Hyperbolic Functions  
%m displays a menu of hyperbolic functions  
(sinh, sinh-1, cosh, cosh-1, tanh, tanh-1). Angle modes  
do not affect hyperbolic calculations.  
³
Problem  
Given the hyperbolic function  
y=3cosh(x-1)  
Find the value of y when x=2 and x=5. Round off results  
to one decimal place. Use the Stored Operations  
function for the repetitive computations.  
OP1=  
N
1
% b ; ? V  
% c < A V  
% t 2 % m " " 2 2  
3
OP2=  
è
3
ß
cosh(2-1  
1
1.54  
Þß  
1.543080634  
1
4.63  
Þß  
27.30823283  
% m " " 5 2 3  
1
81.92  
When x=2, y=4.63; when x=5, y=81.92.  
25  
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Metric Conversions  
Press  
the metric system into the English system and vice  
versa. Scroll through the choices with and and  
select with .To reverse the direction of the  
conversion, press while the desired item is  
.
to access a menu of 20 conversions from  
"
!
V
%
underlined. If you enter a negative value, enclose it in  
parentheses.  
cm  
ò
in centimeters to inches  
cm  
P
Q
2.54  
2.54  
0.3048  
0.3048  
0.9144  
0.9144  
1.609344  
1.609344  
inches to centimeters  
in  
m
m
m
ò
ft  
meters to feet  
feet to meters  
P
Q
ft  
ò
yd meters to yards  
m
P
yards to meters  
yd  
Q
km  
ò
mile  
kilometers to miles  
miles to kilometers  
kmP  
mileQ  
l
ò
gal liters to U.S. liquid gallons l  
P
3.785411784  
3.785411784  
lP4.54609  
(US) U.S. liquid gallons to liters gal  
Q
lò  
gal liters to U.K. gallons  
(UK)  
U.K. gallons to liters  
gal  
Q4.54609  
km/h  
m/s  
ò
kilometers per hour to  
meters per second  
kmàh  
P
3.6  
meters per second to  
kilometers per hour  
m
g
à
s
Q
3.6  
g
ò
oz grams to ounces  
P
28.349523125  
avoirdupois  
ounces avoirdupois to  
grams  
oz  
Q
28.349523125  
kg  
ò
lb kilograms to pounds  
kg  
lb  
P
Q
.45359237  
.45359237  
pounds to kilograms  
éCòéF  
Celsius to Fahrenheit  
Fahrenheit to Celsius  
°C  
(°F  
Q
-
9/5 + 32  
32)  
Q
5/9  
26  
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³
Problem  
Convert 10 kilometers into miles. Then convert 50 miles  
into kilometers. Round results to two decimal places.  
&
Ýkm  
ò
mile  
1 0 . " " "  
ß
10 km mile  
Þ
V V % t 2  
6.21  
ß
50 mile  
Þ
km  
5 0 . " " " % V  
80.47  
V
³
Problem  
Under a pressure of one atmosphere, ethyl alcohol  
freezes at L117éC and boils at 78.5éC. Convert these  
temperatures to the Fahrenheit scale.  
ÝéC/éF  
N J 1 1 7 O . !  
ß
(L  
117)  
é
C
L
Þé  
178.60  
V V  
ß
78.5  
é
C F  
Þé  
# 7 8 I 5 ' ' V  
173.30  
Ethyl alcohol freezes at  
L178.6éF and boils at 173.3éF  
at one atmosphere of pressure.  
27  
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Physical Constants  
Press %] to access a menu of 16 physical  
constants. Scroll through the choices with  
"
and  
!.  
Constant  
Value  
c
g
speed of light  
299792458 meters per second  
9.80665 meters per second2  
gravitational  
acceleration  
10 34 Joule  
-
h
Planck’s constant 6.62606876  
Q
Q
seconds  
N
R
Avogadro’s number 6.02214199  
per mole  
1023 molecules  
A
ideal gas constant 8.314472 Joules per mole  
°Kelvin  
10 31 kilograms  
-
m
electron mass  
9.10938188  
1.67262158  
1.67492716  
Q
Q
Q
Q
e
10 27 kilograms  
-
mp proton mass  
10 27 kilograms  
-
mn neutron mass  
10 28 kilograms  
-
m
m
muon mass  
1.88353109  
G
universal  
gravitation  
6.673  
Q
10 11 Newton meters2  
-
per kilogram2  
F
Faraday constant 96485.3415 coulombs per mole  
10 11 meters  
10 15 meters  
-
ao Bohr radius  
5.291772083  
Q
-
re classical electron 2.817940285  
Q
radius  
-
23  
k
Boltzmann constant 1.3806503  
Q
10  
Joules per  
éK  
-
e
u
electron charge  
1.602176462  
Q
10 19 coulombs  
atomic mass unit 1.66053873  
Q
10 27 kilograms  
-
As you scroll through the menu, the value of the  
underlined constant appears in the result line. When  
you press  
V, the name of the underlined constant  
is transferred to the entry line at the cursor.  
28  
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³
Problem  
A brick falls off the roof of a building and hits the  
sidewalk 3.5 seconds later. Find the height of the  
building in meters and then in feet, rounded off to the  
nearest whole number.  
The formula for distance fallen is  
y= L 12 gt 2  
where t= time in seconds, and g=gravitational  
acceleration (9.80665 meters per second-squared). We  
measure the y coordinate from the position where the  
brick began its fall, and we specify that y is positive  
upwards.  
L
1ç2è  
J 1 1 2 <  
% ] "  
V V  
c
g
h
NA RÞ  
9.80665  
ß
M
1ç2èg  
L
4.903325  
ß
Ansè  
3.52  
< 3 I 5 P V  
% t 0  
L
60.06573125  
ß
Ans  
è
3.52  
L
60.  
ß
Ans mÞft  
. " V V  
L
197  
The height of the building is 60 meters or 197 feet.  
29  
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Integrals  
The TI-36X  
ü
performs numerical integration using  
Simpsons Rule. To prepare for an integral, store the  
lower limit in memory variable A, the upper limit in  
memory B, and the number of intervals (from 1 to 99) in  
memory C. Press  
0
and enter the expression, using  
memory variable A as the independent variable. Then  
press  
data,  
V
µ
. While the calculator is processing the  
CALC displays. When the calculation is  
will return the  
successfully completed, the TI-36X  
ü
numerical value to the result line. In addition, the  
calculator will clear memory variable C; A and B will be  
equal to the upper limit. If A>B, or if C is not an integer  
1-99, or if A, B, or C is undefined, Integrate Error will  
display, and A, B, and C will be cleared.  
If you want to solve a given problem again using a  
different number of intervals or different limits, enter  
values to store in memory variables A, B, and C. Then  
scroll to the integration problem in history and press  
V
the new data.  
; the calculator will solve the same problem with  
The time the calculator takes to solve the problem  
depends on the complexity of the problem and the  
number of intervals. You can abort the calculation by  
pressing and holding  
displayed.  
T
until Integrate Error is  
With polynomials up to the third degree, Simpsons rule  
yields the exact answer, so increasing the number of  
intervals will not change the results. However, with  
polynomials of higher degree and equations containing  
more complicated functions (such as trigonometry),  
increasing the number of intervals will improve the  
precision of the results.  
Note: When you perform integration with trigonometric  
functions, the calculator must be in radian mode.  
30  
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³
Problem  
å/2  
Find  
sin a + cos a da , using 10 intervals.  
0
Solve the problem again, using 20 intervals.  
ß
0ÞA  
& " V 0 S V  
5 = 2 S " V  
1 0 S " " V  
0.  
ß
åñ  
2ÞB  
1.570796327  
ß
10Þ  
C
10.  
µ
CALC  
0 e V R O :  
e " " V R O  
V
Þß  
sin(A)+cos  
2.000000423  
ß
20ÞC  
0 S V 5 = 2 S "  
V 2 0 S " " V  
20.  
µ
CALC  
0 e V R O :  
e " " V R O  
V
Þß  
sin(A)+cos  
2.000000026  
31  
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Probability  
Press %6 to access a menu of functions.  
nPr  
Calculates the number of possible  
permutations of n items taken r at a time.  
The order of objects is important, as in a race.  
nCr  
Calculates the number of possible  
combinations of n items taken r at a time.  
The order of objects is not important, as in a  
hand of cards.  
!
The factorial of n is the product of the positive  
integers from 1 to n. n must be a positive  
whole number 69.  
RAND Generates a random real number between 0  
and 1. To control a sequence of random  
numbers, store an integer (seed value)  
0 to  
S
E. The seed value changes randomly  
every time a random number is generated.  
RANDI Generates a random integer between two  
integers, A and B, where A  

RANDI  

B.  
Separate the two integers with a comma.  
For nPr and nCr, enter the first argument, press  
%6, select nPr or nCr, press  
the second argument.  
V, and enter  
32  
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³
Problem  
n!  
r!(n-r)!  
Compute  
where n=52 and r=5.  
Þ
nPr nCr  
!
5 2 % 6 " "  
ß
52!  
52!  
V
&ß  
ñ
(5!  
è
(52  
= N 5 % 6 " " V <  
N 5 2 ; 5 O % 6 " " O  
V
2598960.  
You no doubt recognize the above formula to find the  
number of possible combinations of n objects taken r at  
a time without replacement. You can obtain this result  
more directly by using nCr on the Probability menu.  
³
Problem  
How many ways can you deal 5 cards from a deck of 52  
cards?  
Þ
nPr nCr  
!
5 2 % 6 "  
ß
52 nCr 5  
5 V  
2598960.  
There are 2598960 ways to deal 5 cards from a deck of  
52 cards.  
33  
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Statistics  
%f displays a menu.  
1-VAR  
Analyzes data from 1 set of data with 1  
measured variable: x.  
LIN  
Analyzes paired data with 2 measured  
variables: x, the independent variable,  
and y, the dependent variable. Yields  
regression equation in the form y=a+bx.  
LN  
Analyzes paired data with 2 measured  
variables. Yields regression equation in  
the form y=a+b ln x.  
EXP  
PWR  
Analyzes paired data with 2 measured  
variables. Yields regression equation in  
the form y=abx.  
Analyzes paired data with 2 measured  
variables. Yields regression equation in  
the form y=axb.  
CLRDATA Clears data values without exiting STAT  
mode.  
You can enter up to 42 points or data pairs.  
When using the LN regression, you do not need to find  
the natural logarithms of the numbers. Enter the data  
directly, and the TI-36X  
ü
makes the transformation.  
Similarly, when you want to make a prediction with the  
LN regression equation, you enter the value of x directly  
(and not ln x), and the calculator returns the predicted  
value of y (and not ln y).  
34  
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To set up the problem and perform the analysis:  
1. Press %f. Select the desired type of analysis  
from the menu and press  
indicator displays.  
V. The STAT  
2. Press  
7.  
3. Enter a value for X1 and press  
$.  
4. Then:  
In 1-VAR stat mode, enter the frequency of  
occurrence (FRQ) of the data point and press  
$
. FRQ default=1. If FRQ=0, the data point is  
ignored. Or,  
In LIN, LN, EXP, OR PWR, enter the value of Y  
and press  
$.  
5. Repeat steps 3 and 4 until all data points are  
entered. You can change or delete data points by  
scrolling to the desired point and editing or pressing  
'
. If you are in 2-VAR mode, you must delete  
both the data point and the frequency. You can add  
new points by scrolling to the last point and pressing  
$
; the calculator will prompt you for the new data.  
If you add or delete data points, the TI-36X  
automatically reorders the list.  
ü
6. When all points and frequencies are entered:  
Press  
8
to display the menu of variables  
(see table for definitions) and their current  
values. Or,  
Press  
7
to return to the blank STAT screen.  
You can perform calculations with data variables (  
ô,  
õ
, etc.). After such calculations, you can return to  
the display of variables by pressing  
8
again.  
You can return to the data entries again by pressing  
7
.
35  
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7. When finished:  
Press %f and select CLRDATA to clear  
all data points without exiting STAT mode, or  
Press %h to access the following  
menu.  
EXIT ST: Y  
N
Press  
V
when Y (yes) is underlined to clear  
all data values and exit STAT mode. STAT  
indicator turns off.  
Press  
V
when N (no) is underlined to return  
to the previous screen without exiting STAT  
mode.  
Variables  
Definition  
n
Number of X or (X, Y) data points.  
Mean of all X or Y values.  
Sample standard deviation of X or Y.  
Population standard deviation of X or Y.  
Sum of all X or Y values.  
ô
or  
Sx or Sy  
x or  
õ
ó
ó
y
÷
÷
÷
a
b
r
x or  
x2 or  
xy  
÷
y
÷
y2  
Sum of all X2 or Y2 values.  
Sum of X*Y for all XY pairs.  
Linear regression Y-intercept.  
Linear regression slope.  
Correlation coefficient.  
X
ê
ê
(2-VAR)  
Calculates predicted X value when you  
input a Y-value.  
Y
(2-VAR)  
Calculates predicted Y value when you  
input an X value.  
36  
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³
Problem  
The table below gives the Gross Domestic Product per  
capita and the telephone density (main lines per 100  
population) for several countries in a recent year.  
Country  
Austria  
Israel  
Argentina  
Brazil  
GDP/Cap.  
$25032  
$13596  
$ 8182  
$ 3496  
Tel. Den.  
46.55  
41.77  
15.99  
7.48  
China  
$
424  
3.35  
Using the LIN regression, find the equation representing  
the best fit, in the form y=a+bx, where x=GDP/capita  
and y=telephone density. Find the coefficient of  
correlation. Use this equation to predict the telephone  
density of a country with a GDP per capita of $10,695. If  
a country has a telephone density of 5.68, what GDP  
per capital would you expect this country to have?  
X1=25032  
Y1=46.55  
Y3=15.99  
Y5=3.35  
ø
ø
ø
ø
% t 4 % f " V  
7 2 5 0 3 2  
$ 4 6 I 5 5  
$ 1 3 5 9 6 $ 4 1 I 7 7  
$ 8 1 8 2 $ 1 5 I 9 9  
$ 3 4 9 6 $ 7 I 4 8 $ 4 2 4  
$ 3 I 3 5  
37  
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Ý
Ý
Ý
Þ
÷
xy  
÷
xy  
÷
xy  
a
a
a
b
r
8 ! ! ! ! !  
3.5143  
Þ
b
r
"
0.0019  
Þ
b
r
"
0.9374  
Ýx' y'  
" "  
y'(10695)  
x'(5.68)  
1 0 6 9 5 O V % t 2  
24.08  
1126.  
8 ! ! 5 I 6 8 O V  
% t 0  
The equation is y=3.5143+0.0019x. The coefficient of  
correlation is .9374. A country with a GDP per capita of  
$10695 is predicted to have a telephone density of  
24.08. If a country has a telephone density of 5.68, you  
would expect that country to have a GDP per capita of  
about $1126.  
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Boolean Logic Operations  
Press  
-
operations.  
to access a menu of Boolean Logic  
Function  
AND  
Effect on Each Bit of the Result  
0 AND 0 = 0  
0 OR 0 = 0  
0 XOR 0 = 0  
NOT 0 = 1  
0 AND 1 = 0  
0 OR 1 = 1  
0 XOR 1 = 1  
NOT 1 = 0  
1 AND 1 = 1  
1 OR 1 = 1  
1 XOR 1 = 0  
OR  
XOR  
NOT  
2s  
2s complement  
Except for NOT and 2s complement, these functions  
compare the corresponding bits of two values. The  
result is displayed in the current number base.  
You can perform logical operations in the decimal,  
octal, and hexadecimal modes.  
³
Examples  
Perform the operations 9 AND 2, 9 OR 2, and 9 XOR 2.  
Þ
and or xor  
9 and 2  
9 -  
ß
2 V  
0.  
ß
9 or 2  
9 - " 2 V  
9 - " " 2 V  
11.  
ß
9 xor 2  
11.  
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Number-System Modes  
Number system modes are second functions of keys.  
%| Selects decimal mode (default). When the  
calculator is in another number mode,  
press %| to return the calculator to  
decimal mode. Note: Normally you should  
keep the calculator in the decimal mode,  
because some of the calculators operating  
features are limited or nonexistent in the  
other modes.  
%~ Selects octal mode. You can enter positive  
octal numbers as large as 3777777777.  
Numbers beyond this are interpreted as  
negative.  
%} Selects hexadecimal mode. You can enter  
positive hexadecimal numbers as large as  
7FFFFFFFFF. Numbers beyond this are  
interpreted as negative.  
To enter the hexadecimal digits A through F, press  
and then the appropriate key shown below.  
%
D
E
F
B C D  
A
B
C
E F G  
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³
Problem  
Add 456+125 in base 8 and in hexadecimal. Then  
return the calculator to decimal mode and do the same  
addition.  
ß
456+125  
456+125  
456+125  
% ~ 4 5 6 : 1 2 5 V  
603  
ß
% } # V  
57b  
ß
% | # V  
581.  
Complex Numbers  
Enter a complex number as an ordered pair in  
parentheses, with the real part first. Operations with  
complex numbers are limited to , and  
:
,
;
,
<
,
=
,
J
the functions in the menu below. When you perform  
computations with complex numbers, the result line  
displays the real part of the answer, and r shows on the  
indicator line; press  
"
to see the imaginary part, and i  
shows on the indicator line.  
If a computation with complex numbers yields a real  
number, the r and i will no longer be displayed.  
When you store a complex number in memory, it takes  
up two memory locations. Store to memory variable A,  
and it occupies A (for the real part) and B (for the  
imaginary part); or store to C, and it occupies C and D.  
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Press %\ to access a menu.  
conj Returns the conjugate of a complex number.  
real  
Returns the real part of a complex number.  
imag Returns the imaginary part of a complex  
number.  
abs  
Returns the absolute value of a number.  
³
Problem  
Find the product of (4-2i) and (3+5i); display the  
imaginary part as well as the real part of the result.  
Then find the conjugate of the result, and display the  
imaginary part as well as the real part.  
Þß  
(4,L  
2)è  
(3,5  
N 4 % i J 2 O < N 3 %  
i 5 O V  
22.  
14.  
r
Þß  
(4,L  
2)è  
(3,5  
"
i
Þ
conj real  
% \  
ß
conj(22,14)  
2 2 % i 1 4 O V  
22.  
r
ß
conj(22,14)  
"
M
14.  
i
42  
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Error Conditions  
When Error appears in the display, the calculator will  
not accept a keyboard entry until you press  
4
once to clear the error  
or  
%r. Press  
4
message and return to the entry that caused the error;  
then you can edit the entry or clear the display.  
ARGUMENT  
-
a function does not have the correct  
number of arguments.  
DIVIDE BY 0  
-
You attempted to divide by 0.  
In statistics, n=1.  
SYNTAX  
-
The command contains a syntax error:  
entering more than 23 pending operations, 8 pending  
values, or having misplaced functions, arguments,  
parentheses, or commas.  
EQU LENGTH  
-
An entry exceeds the limit (88  
characters or items for Entry Line and 47 for Stat or  
Stored Operation lines).  
OP  
-
Pressing  
2
or  
3
when constants not defined  
or while in STAT mode.  
OVERFLOW  
-
The result is outside the range of the  
calculator:  
In decimal, range |M  
1ä  
10100 or  
{1ä  
10100  
.
In Hex, range 0-7FFFFFFFFF, 8000000001-  
FFFFFFFFFF.  
In Oct, range 0-3777777777, 4000000001-  
7777777777  
FRQ DOMAIN  
-
FRQ value (in 1-VAR stats) < 0 or >99,  
or not an integer.  
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DOMAIN  
-
You specified an argument to a function  
outside the valid range. For example:  
For x  
: x=0; y<0 and x not an odd integer.  
For yx: y and x=0; y<0 and x not an integer.  
For  
x, x<0.  
For x!: x is not an integer between 0 and 69.  
For Boolean and, or, xor: x or y in Hex out of range  
(>239).  
For log or ln: x  
0.  
For tan: x=90 , -90¡, 270¡, -270¡, 450¡, etc.  
¡
For sin-1 or cos-1: |x| > 1.  
For tanh-1(x): |x|>1.  
For cosh-1 (0).  
For cosh-1(x): x<0.  
For nCr or nPr: either n or r is not an integer  
|
0.  
|
æ
|
1E10, where  
æ
is an angle in a trig or  
P4  
Rx(, P4Ry( function.  
STAT  
-
Pressing  
When not in STAT mode, pressing  
or %h  
Using a complex number incorrectly in an  
operation or in memory.  
BASE Using a base incorrectly or in the wrong mode.  
INTEGRATE Error in setting up integration problem:  
8
with no defined data points.  
7
,
8,  
.
COMPLEX  
-
-
-
A>B, or  
C not integer 1-99, or  
A, B, or C undefined.  
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In Case of Difficulty  
Review instructions to be certain calculations were  
performed properly.  
Press  
T
and  
4
simultaneously to reset. When  
released, memory and settings are cleared, and  
MEM CLEARED is displayed.  
Check the battery to ensure that it is fresh and properly  
installed.  
Change the battery when:  
T
does not turn the unit on, or  
The screen goes blank, or  
You get unexpected results.  
Battery Replacement  
Replace protective cover. Place the TI-36X  
down.  
ü
face  
1. Remove screw case, using a small Phillips  
screwdriver.  
2. Carefully separate front from back, starting from the  
bottom. Caution: Be careful not to damage any  
internal parts.  
3. Remove battery, using a small Phillips screwdriver,  
if necessary; replace with new battery. Install  
batteries according to polarity (+ and -) diagrams.  
Caution: Avoid contact with other TI-36X  
components while changing the battery.  
ü
4. If necessary, press  
T
and  
4
simultaneously  
to reset. When released, memory and settings are  
cleared, and MEM CLEARED is displayed.  
5. Properly dispose of used batteries immediately. Do  
not leave them within the reach of children.  
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Service Information  
TI Product and Services Information  
For more information about TI products and services,  
contact TI by e-mail or visit the TI calculator home page  
on the world-wide web.  
e-mail address:  
Internet address:  
education.ti.com  
Service and Warranty Information  
For information about the length and terms of the  
warranty or about product service, refer to the warranty  
statement enclosed with this product or contact your  
local Texas Instruments retailer/distributor.  
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