TI-36X
ý
Scientific Calculator
USER’S GUIDE
2000, 2003 Texas Instruments Incorporated
education.ti.com
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48
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.
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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
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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.
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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.
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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.
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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 2’s
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.
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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.
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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
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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.
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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
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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.
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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
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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
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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).
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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.
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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
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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.
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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.
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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.
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Integrals
The TI-36X
ü
performs numerical integration using
Simpson’s 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, Simpson’s 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.
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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
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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
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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.
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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).
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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
.
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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.
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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
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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
2’s
2’s complement
Except for NOT and 2’s 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 calculator’s 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
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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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