TI-36X
Scientific Calculator
ý
USER’S GUIDE
2000, 2003 Texas Instruments Incorporated
education.ti.com
ti-cares@ti.com
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Table of Contents
Turning the Calculator On and Off............................1
Alternate Functions...................................................1
Display......................................................................2
Scrolling....................................................................2
Menus.......................................................................3
Fix.............................................................................3
Clearing, Correcting, and Resetting .........................4
Display Indicators .....................................................5
Order of Operations..................................................6
Basic Operations ......................................................7
Last Answer..............................................................7
Percent .....................................................................9
Fractions.................................................................10
Exponents, Roots, and Reciprocals .......................11
Notation ..................................................................12
Pi ............................................................................13
Memory...................................................................14
Stored Operations ..................................................16
Logarithms..............................................................18
Trigonometric Functions .........................................20
Angle Modes...........................................................22
Rectangular
Hyperbolic Functions ..............................................25
Metric Conversions.................................................26
Physical Constants .................................................28
Integrals..................................................................30
Probability...............................................................32
Statistics .................................................................34
Boolean Logic Operations ......................................39
Number-System Modes..........................................40
Complex Numbers..................................................41
Error Conditions......................................................43
In Case of Difficulty.................................................45
Battery Replacement ..............................................45
Service Information.................................................46
Polar ................................................ 24
/
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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-36X ü, press
•
memory is retained.
APD
(Automatic Power Downé) turns off the
é
TI-36X
automatically if no key is pressed for about
ü
five minutes. Press
the display, pending operations, settings, and memory
are retained.
after APD to power up again;
T
%r
. All data in
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.
2nd function
ì
Primary function
Press % to activate the second function of a key. To
cancel the second function before making an entry,
press
shown in brackets ([ ]). For example, press
the square of a number. Press
square root of a number.
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again. In this manual, second functions are
%
1
P
%n
to find
P
to find the
Display
The TI-36X ü has a two-line display. The first line
Entry Line
(
items (47 for
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 (
10 digits, plus a decimal point, a negative sign, a
indicator, and a 2-digit positive or negative exponent.
Results that exceed the digit limit are displayed in
scientific notation.
Note
are shown in decimal format consistent with the
calculator display.
) displays an entry of up to 88 digits or
Stat
or Stored Operations). Entries begin
Result Line
: In the text, numbers containing decimal fractions
) displays a result of up to
x10
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
to move the cursor to the beginning or end
%!
of the entry.
After an expression is evaluated, press # and
•
to scroll through previous entries, which are stored
in the TI-36X
and press
new expression and return the new result.
history. If you edit a previous entry
ü
, the calculator will evaluate the
V
%"
or
$
2
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Menus
Some key presses access menus: S,
e, -, 8, &, /, .
%p, %d, %^, %m
%], %6, %f, %h
%Z, %t, %\
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
to select the first function before proceeding
V
to the next.
To return to the previous screen without selecting the
menu item, press
4
.
, and
R
,
%q
,
,
%s
,
,
.
Fix
displays a menu:
%t
displayed results, scroll with
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
(default) in the menu, or press
You can specify rounding places before you begin your
calculations, before you complete an operation with
, or after the results are displayed.
V
F0123456789
"
. To round
or ! to select the
%tI
.
F
3
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Clearing, Correcting, and Resetting
Key Action
4
'
%[
%s
"V
or
T&4
(simultaneously)
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.
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.
Error
If an
•
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.
Resets the TI-36X
. Returns unit to
ü
default settings; clears memory variables,
pending operations, all entries in history,
statistical data,
operations.
Ans
, and stored
MEM CLEARED
is displayed.
4
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Display Indicators
Special indicators may appear in the display to provide
additional information about functions or results.
Indicator Meaning
2nd
FIX
SCI or ENG
STAT
DEG, RAD
GRAD
or
HEX or OCT
x10
#
$
"
!
r or i
µ
2nd function is active.
Calculator is rounding results to
specified number of places.
Scientific or engineering notation is
active.
Calculator is in Statistics mode.
Specifies angle-unit setting (degrees,
,
radians, or grads). The default is the
degree setting.
Calculator is in hexadecimal or octal
mode.
Precedes the exponent in scientific or
engineering notation.
An entry is stored in memory before
and/or after the active screen. Press
and $ to scroll.
An entry or menu list extends beyond
the capacity of the screen. Press
to scroll.
!
"
Complex number, real part, or
complex number, imaginary part.
Calculator is busy.
#
and
5
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Order of Operations
The TI-36X ü uses EOSè (Equation Operating
System) to evaluate expressions.
Order Evaluation
1st Expressions inside parentheses.
2nd Functions which need a ) and precede the
argument, such as
menu items; Boolean Logic
complement.
3rd Fractions.
4th Functions that are entered after the argument,
such as x
metric conversions.
5th Exponentiation (^) and roots (
6th Negation (L).
7th Permutations (
8th Multiplication, implied multiplication, division.
9th Addition and subtraction.
10th Boolean logic
11th
Boolean logic
12th Conversions (
13th
completes all operations and closes all
V
open parentheses.
You can change the order of operations by enclosing
expressions in parentheses.
sin, log
2
and angle unit modifiers (é ê ë
nPr
) and combinations (
AND
.
XOR
and OR.
d
Ab/
/
,
4
/
4F/
c
e
, and all
NOT
and
x
).
‡
D, 4DMS
R
/
2’s
).
P
nCr
r g
);
).
6
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Basic Operations
As you press keys, numerals, operators, and results
appear on the display.
,
H, ?, @, A, B
Enters numerals 0 through 9.
C, D, E, F, G
:, ;, <, =
Adds, subtracts, multiplies,
divides.
N, O
Opens, closes a parenthetical
expression.
I
J
V
Inserts the decimal point.
Enters a negative sign.
Completes all operations.
Last Answer
recalls the value of the most recently
%u
calculated result and enters it into the current entry as
Ans
.
If you press an operator key immediately after
completing an operation with
calculated result is recalled and entered as
, the most recently
V
Ans
.
7
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³
5<9:6;2
<N9:6O;2V
5
V
W887<
%t""""
V
:%u%t
5<2
V
%tI
###
"""'%[8V
%s"V
5è9+6-2
5è(9+6)-2
Ansñ8.7
8.390804598
F0123456789
Ansñ8.7
FIX DEG
5è2+Ans
6
FIX DEG
5è29
2+Ans
5è(9+6)-2
5è(8+6)-2
MEM CLEARED
Examples
ß
49.
DEG
ß
73.
DEG
ß
DEG
DEG
ß
8.391
ß
18.390805
ß
18.3908046
DEG
ø
DEG
ß
68.
DEG
DEG
8
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Percent
To calculate a percent, press
after entering a
%l
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?
5000<3
:
7300<2I3
V
:
8400<3I1
V
<
V
280
%lV
%l
%l
5000è3%
Ans+7300è2.
Ans+8400è3.
Ansè280
150.
DEG
Þß
317.9
DEG
Þß
578.3
DEG
161924.
DEG
ß
ß
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
%`
%_
If a problem contains both fractions and decimals, the
results will be displayed in decimal format.
³
41315:211
V
5
%`V
%_V
<J3110V
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
before entering the first
J
argument.
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.
Examples
1
4ç3ç5+2ç1ç5
ß
6ð4ñ5
DEG
ß
d
c
Ans4Ab/
c
/
34
34ñ5
DEG
3ç10
M
DEG
M
DEG
ß
6.8
ß
2.04
Ans4F34D
Ans
è
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
P:4KN2:1OV
5
%n49OV
%j64V
6
%kV
25
Examples
52+4^(2+1)
DEG
ì
(49)
DEG
x
ì
6
64
DEG
-1
25
DEG
ß
89.
ß
7.
ß
2.
ß
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
1{n<10
and p is an integer.
ENG
: Engineering notation (exponent is a multiple
•
n x 10^p
, where
of 3).
only
These modes affect
the display of results, and not
the internally stored results.
lets you enter a value in scientific notation,
M
regardless of the numeric notation mode. Press
J
before entering a negative exponent.
³
1I2M5+4I6M7
%Z"V
%Z"V
V
Examples
1.2E5+4.6E7
46120000.
DEG
1.2E5+4.6E7
4.612
X10
SCI DEG
1.2E5+4.6E7
46.12
X10
ENG DEG
ß
ß
07
ß
06
12
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Pi
enters the value of p. It is stored internally to 13
5
digits (
3.141592653590
(
3.141592654
When multiplying
press
; multiplication is implicit.
<
³
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
Fix
Use the
function to display results rounded to the
nearest whole number.
%t"V25<
V
#'"""PV
#%[4V
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.
) and displayed to 10 digits
).
by a number, you do not need to
p
r; area =pr 2; surface area=(4p)r 2.)
p
2
5
è
5
p
FIX DEG
2
5
è
p
FIX DEG
2
4
5
è
p
FIX DEG
Examples
ß
31.
ß
79.
ß
314.
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
%q
R
%p
When you press S, a menu of variables displays:
A, B, C, D
Press
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
V
expression and store the resulting value to the memory
variable you select.
Press
variables. Press
to recall and press
inserted into your current entry at the cursor.
Pressing
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.
Lets you store values to variables.
Recalls the values of variables.
Recalls variables by letter designation.
Displays menu:
Select Y (yes) and press
CLR VAR: Y N
V
.
to clear
all memory variables and re-initialize
seed in E.
, and E. Press
, and the value of your last answer is
V
or ! to select a variable.
"
and then
S
, the TI-36X ü will simultaneously evaluate the
to display the menu of memory
%q
or ! to select the variable you wish
"
. The value in this variable is
V
also displays the menu of memory
R
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In addition to serving as a memory variable,
stores a
E
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.
%Z""V
SV
560
340<610
150
210
150
210
S"V
<%qVV
<%qVV
<R"VV
<R"VV
350
350è560"A
<
340è610"B
150è196000
210è196000
150èB
210èB
ENG DEG
ENG DEG
ENG DEG
ENG DEG
ENG DEG
ENG DEG
196.
207.4
29.4
41.16
31.11
43.554
ß
03
x10
ß
03
x10
ß
06
x10
ß
06
x10
ß
06
x10
ß
06
x10
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
Op1
The TI-36X ü stores two operations,
Op1
or
%c
or
Op2
and recall it:
.
store an operation to
1. Press
%b
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
to save the operation to memory.
V
4. Each subsequent time you press
TI-36X
recalls the stored operation and applies it
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
Op2
or
.
You can set the TI-36X
to display only the counter
ü
and the result, and not the expression on the entry line.
Press
highlighted (
or
%b
) and press V. Repeat to toggle this
û
, press ! until the = is
%c
setting off.
and
or 3, the
2
Op2
. To
Op1
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³
%b<2V
2
3
2
2
%c:5V
3
10
3
3
2
3
Examples
OP1=è2
DEG
3è2
16.
6è2
2 12.
12è2
3 24.
ß
DEG
ß
DEG
ß
DEG
OP2=+5
DEG
10+5
1 15.
15+5
2 20.
20+5
3 25.
25è2
1 50.
50+5
1 55.
ß
DEG
ß
DEG
ß
DEG
ß
DEG
ß
DEG
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Logarithms
displays a menu of log functions.
%d
log
Yields the common logarithm of a number.
^
10
Raises 10 to the power you specify.
ln
Yields the logarithm of a number to the base
(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
%d
OV
100
%d"3I2OV
log 10
log(100)
10^(3.2)
1584.893192
%d""9I
453
V
%d!4I7OV
O
ln(9.453)
2.246332151
e^(4.7)
109.9471725
e
Examples
Þ
^
DEG
ß
2.
DEG
ß
DEG
ß
DEG
ß
DEG
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³
A radioactive substance decays exponentially. If y
grams of certain radioactive substance are initially
Problem
o
present, the number of grams y(t) after t days is given
by the formula:
-0.00015t
y(t)=y
e
o
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.
J0I
<%d"""V
5
R<
%t
<%d"""V
5
R<
00015
340
2
475
SV
OV
OV
L
0.00015ÞA
5èe^(Aè340)
4.751393353
5è e^(Aè340)
FIX DEG
5èe^(Aè475)
FIX DEG
L
0.00015
DEG
DEG
4.75
4.66
ß
ß
ß
ß
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
displays a menu of the trigonometric functions
e
-1
sin, sin
(
,
select the desired function, enter the value, and close
the parentheses with
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
³
e""
O%t4V
30
e"
0I7391
e""Ve!1O
OV
-1
cos, cos
tan, tan
,
.
O
-1
). Press " or ! to
(page 22) for other angle modes.
Ý
cos cos
cos(30)
FIX DEG
sin sin
FIX DEG
-1
0.7391
sin
OV
(
FIX DEG
cos(tan-1(1)
FIX DEG
Examples
-1
Þ
DEG
ß
0.8660
Þ
-1
Þß
47.6548
Þß
0.7071
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48
³
a
Find angle
length of the hypotenuse
in the right triangle below. Then find the
h
and angle b. Measurements
Problem
of length and height are in meters. Round off results to
one decimal place.
h
b
3
a
7
L
Remember 3/7=tan
so
h
=3/sin a. Then 7/h=sin b, so b=sin
a
%t1e!3=7O
V
e%uOV
=%uV
3
e"7=%uOV
, so a=tan
1
(3/7). Then 3/h=sin a,
L
1
(7/h).
tan-1(3ñ7)
FIX DEG
sin(Ans)
FIX DEG
3ñAns
FIX DEG
sin-1(7ñAns)
FIX DEG
ß
23.2
ß
0.4
ß
7.6
ß
66.8
Angle a is about 23.2 degrees. The hypotenuse
about 7.6 meters. Angle
b
is about 66.8 degrees.
h
is
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Angle Modes
displays a menu to specify the angle unit modifier
/
for an entry: degrees (
ê
(
). It also lets you convert an angle to DMS
é
ë
Notation (
DMS
4
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
Two adjacent angles measure 12
26
, respectively. Sum the two angles and
é54ê38ë
display the results in DMS format.
/
12
31
/"46/"":
26/54
VV
/!VV
), radians (r), grads (g), or DMS
é
).
é31ê45ë
/"38/""
Problem
and
ê ë r g
é
12é31
12é31ê46ë+
12é31ê46ë+2
Ans4DMS
39é26ê24
DEG
DEG
DEG
Þß
39.44
DEG
DEG
Þ
ß
ë
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displays a menu (
&
DEG RAD GRD
) to express
angle measurements in degrees (default), radians, or
grads, respectively.
³
You probably know that 30
Degree Mode, find the sine of 30
/6 radians. In the default
é=å
. Then set the
é
calculator to Radian Mode and find the sine of
Problem
/6
å
radians.
DEG
RAD
ß
0.5
ß
0.5
e30OV
&"V"5=6O
V
sin(30)
sin(åñ6)
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
é
find the sine of
e30/OV
&!V"N5=6O
/"""OV
/6 radians.
å
sin(30é)
sin((åñ6)
ß
0.5
RAD
ß
r
)
0.5
DEG
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Rectangular/Polar
displays a menu to convert rectangular
%^
coordinates (x, y) to polar coordinates (r,
versa. For each coordinate to which you are converting,
enter both values expressed in the format
you are converting, separated by a comma, then close
the parentheses with
operation with
before you complete the
O
. Set angle mode, as necessary,
V
before starting calculations.
³
Convert polar coordinates (r,
)=(5, 30) into rectangular
æ
coordinates. Then convert rectangular coordinates
(x, y)=(3, 4) into polar coordinates. Round all results to
1 decimal place.
%^""5%i30O
%t""VV
%^"""5%i
30
OV
%^3%i4OV
%^"3%i4O
V
(r, q)=(5, 30) converts to (x, y)=(4.3, 2.5). (x, y) = (3, 4)
converts to (r,
)=(5.0, 53.1).
q
) or vice
æ
from
which
Examples
P4Rx(5,30)
FIX DEG
P4Ry(5,30)
FIX DEG
R4Pr(3,4)
FIX DEG
R4Pq(3,4)
FIX DEG
ß
4.3
ß
2.5
ß
5.0
ß
53.1
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Hyperbolic Functions
displays a menu of hyperbolic functions
%m
sinh, sinh
(
do not affect hyperbolic calculations.
³
Given the hyperbolic function
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.
%b;?V
%c<AV
%t2%m""22
3
%m""523
When x=2, y=4.63; when x=5, y=81.92.
-1
cosh, cosh
,
-1
tanh, tanh
,
y=3cosh(x-1)
-1
). Angle modes
Problem
OP1=N1
DEG
OP2=è3
DEG
cosh(2-1
1 1.54
FIX DEG
1.543080634
1 4.63
FIX DEG
27.30823283
1 81.92
FIX DEG
ß
Þß
Þß
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Metric Conversions
Press
to access a menu of 20 conversions from
.
the metric system into the English system and vice
versa. Scroll through the choices with
select with
conversion, press
.To reverse the direction of the
V
while the desired item is
%
and ! and
"
underlined. If you enter a negative value, enclose it in
parentheses.
cm
in
centimeters to inches
ò
inches to centimeters
mòft
meters to feet
feet to meters
mòyd
meters to yards
yards to meters
km
kilometers to miles
ò
mile
miles to kilometers
lògal
liters to U.S. liquid gallons
(US)
U.S. liquid gallons to liters
lògal
liters to U.K. gallons
(UK)
U.K. gallons to liters
km/h
kilometers per hour to
ò
m/s
meters per second
meters per second to
cm
2.54
P
in
2.54
Q
m
0.3048
P
ft
0.3048
Q
m
0.9144
P
yd
0.9144
Q
km
1.609344
P
mile
1.609344
Q
l
3.785411784
P
gal
3.785411784
Q
l
4.54609
P
gal
4.54609
Q
km
3.6
àhP
m
3.6
àsQ
kilometers per hour
gòoz
grams to ounces
g
28.349523125
P
avoirdupois
ounces avoirdupois to
grams
kgòlb
kilograms to pounds
pounds to kilograms
F
Celsius to Fahrenheit
éCòé
Fahrenheit to Celsius
oz
Q
28.349523125
kg
.45359237
P
lb
.45359237
Q
°C
9/5 + 32
Q
(°F
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.
."""
10
VV%t
."""%V
50
V
Ý
kmòmile
2
10 kmÞmile
FIX DEG
50 mileÞkm
FIX DEG
&
DEG
ß
6.21
ß
80.47
³
Problem
Under a pressure of one atmosphere, ethyl alcohol
freezes at
117éC and boils at 78.5éC. Convert these
L
temperatures to the Fahrenheit scale.
Ý
é
é
C
F
NJ
117
O.!
VV
#78I5''V
/
FIX DEG
(L117) éC
L
FIX DEG
78.5 é CÞéF
FIX DEG
Þé
178.60
173.30
ß
ß
Ethyl alcohol freezes at L178.6éF and boils at 173.3éF
at one atmosphere of pressure.
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Physical Constants
Press
%]
constants. Scroll through the choices with
Constant
speed of light
c
gravitational
g
to access a menu of 16 physical
and !.
"
Value
299792458 meters per second
9.80665 meters per second
2
acceleration
34
Planck’s constant
h
6.62606876Q 10
-
Joule
seconds
Avogadro’s number
N
A
ideal gas constant
R
6.02214199Q 10
per mole
8.314472 Joules per mole
23
molecules
°Kelvin
31
electron mass
m
e
proton mass
m
p
neutron mass
m
n
muon mass
m
m
universal
G
gravitation
Faraday constant
F
Bohr radius
a
o
classical electron
r
e
radius
Boltzmann constant
k
electron charge
e
atomic mass unit
u
9.10938188Q 10
1.67262158Q 10
1.67492716Q 10
1.88353109Q 10
6.673 Q 10
per kilogram
96485.3415 coulombs per mole
5.291772083Q 10
2.817940285Q 10
1.3806503Q 10
K
é
1.602176462Q 10
1.66053873Q 10
-
kilograms
27
-
kilograms
27
-
kilograms
28
-
kilograms
11
-
Newton meters
2
11
-
meters
15
-
meters
23
-
Joules per
19
-
coulombs
27
-
kilograms
2
As you scroll through the menu, the value of the
underlined constant appears in the result line. When
you press
, the name of the underlined constant
V
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
2
1
t
y=
g
L
2
where t= time in seconds, and g=gravitational
acceleration (
measure the
brick began its fall, and we specify that
9.80665
meters per second-squared). We
y
coordinate from the position where the
y
is positive
upwards.
è
L
J112<
%]"
VV
<3I5PV
%t
0
."VV
1ç2
DEG
c g h NA R
9.80665
DEG
M
1ç2èg
L
4.903325
DEG
2
Ansè3.5
L
60.06573125
DEG
2
Ansè3.5
L
FIX DEG
Ans mÞft
L
FIX DEG
Þ
ß
ß
ß
60.
ß
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
memory variable A as the independent variable. Then
press
data,
. While the calculator is processing the
V
CALC
µ
successfully completed, the TI-36X
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,
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
; the calculator will solve the same problem with
V
the new data.
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.
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
and enter the expression, using
0
displays. When the calculation is
will return the
ü
will
is
mode.
T
until
Integrate Error
Integrate Error
radian
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48
³
/2
å
Find
sin a + cos a da , using 10 intervals.
⌠
⌡
0
Solve the problem again, using 20 intervals.
&"V0SV
5=2S"V
S""V
10
0eVRO:
e""VRO
V
SV5=2S"
0
V20S""V
0eVRO:
e""VRO
V
Problem
0ÞA
åñ2Þ
B
1.570796327
10ÞC
µ
CALC
‰
sin(A)+cos
2.000000423
20ÞC
µ
CALC
‰
sin(A)+cos
2.000000026
RAD
RAD
RAD
RAD
RAD
RAD
RAD
RAD
10.
20.
ß
0.
ß
ß
Þß
ß
Þß
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Probability
Press
nPr
to access a menu of functions.
%6
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.
!
RAND
factorial
The
integers from 1 to
whole number
n
is the product of the positive
of
n. n
must be a positive
69.
Generates a random real number between 0
and 1. To control a sequence of random
numbers, store an integer (
E. The
S
seed value
seed value
changes randomly
every time a random number is generated.
RANDI
Generates a random integer between two
A
integers,
and B, where A
RANDI
Separate the two integers with a comma.
nPr
For
%6
nCr
and
, enter the first argument, press
nPr
, select
nCr
or
, press V, and enter
the second argument.
) ‚ 0 to
B.
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³
Compute
52
n!
where n=52 and r=5.
r!(n-r)!
%6""
V
=N5%6""V<
N52;5O%6""O
V
Problem
nPr nCr !
DEG
52!
DEG
52!ñ(5!è(52
2598960.
DEG
Þ
ß
&
ß
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
³
nCr
on the
Probability
menu.
Problem
How many ways can you deal 5 cards from a deck of 52
cards?
%6"
52
V
5
nPr nCr !
52 nCr 5
Þ
DEG
ß
2598960.
DEG
There are 2598960 ways to deal 5 cards from a deck of
52 cards.
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Statistics
displays a menu.
%f
1-VAR
LIN
LN
EXP
PWR
CLRDATA
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
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).
Analyzes data from 1 set of data with 1
measured variable: x.
Analyzes paired data with 2 measured
variables:
x
and
, the independent variable,
y
, the dependent variable. Yields
regression equation in the form y=a+bx.
Analyzes paired data with 2 measured
variables. Yields regression equation in
the form y=a+b ln x.
Analyzes paired data with 2 measured
variables. Yields regression equation in
the form y=ab
x
.
Analyzes paired data with 2 measured
variables. Yields regression equation in
the form y=ax
Clears data values without exiting
b
.
STAT
mode.
makes the transformation.
ü
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To set up the problem and perform the analysis:
1. Press
from the menu and press
. Select the desired type of analysis
%f
V
. The
STAT
indicator displays.
2. Press
3. Enter a value for
7
.
and press $.
X
1
4. Then:
In
•
stat mode, enter the frequency of
1-VAR
occurrence (
.
$
FRQ
) of the data point and press
FRQ
default=1. If
=0, the data point is
FRQ
ignored. Or,
In
•
LIN, LN, EXP
and press
$
.
, OR
, enter the value of
PWR
Y
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
'
mode, you must delete
2-VAR
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
ü
automatically reorders the list.
6. When all points and frequencies are entered:
•
Press
to display the menu of variables
8
(see table for definitions) and their current
values. Or,
Press 7 to return to the blank
•
You can perform calculations with data variables (
, etc.). After such calculations, you can return to
õ
the display of variables by pressing
STAT
8
screen.
ô
again.
,
You can return to the data entries again by pressing
.
7
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7. When finished:
Press
•
all data points
Press
•
and select
%f
without
%h
CLRDATA
exiting
to access the following
menu.
EXIT ST: Y
Press
when Y (yes) is underlined to clear
V
all data values and exit
N
STAT
indicator turns off.
Press
when N (no) is underlined to return
V
to the previous screen without exiting
mode.
Variables Definition
n
ô
Sx
ó
÷
÷
÷
a
b
r
X
or
x or
x
x
xy
ê
õ
or
or
2
or
(
2-VAR
Number of X or (X, Y) data points.
Mean of all X or Y values.
Sample standard deviation of X or Y.
Sy
Population standard deviation of X or Y.
ó
y
Sum of all X or Y values.
÷
y
÷
2
y
Sum of all
2
2
or
values.
X
Y
Sum of X*Y for all XY pairs.
Linear regression Y-intercept.
Linear regression slope.
Correlation coefficient.
) Calculates predicted X value when you
input a Y-value.
(
) Calculates predicted Y value when you
ê
2-VAR
Y
input an X value.
mode, or
STAT
mode.
to clear
STAT
STAT
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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
GDP/Cap. Tel. Den.
Austria $25032 46.55
Israel $13596 41.77
Argentina $ 8182 15.99
Brazil $ 3496 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?
%t4%f"V
7
25032
$46I
$
$
$
$3I
55
13596$41I77
8182$15I99
3496$7I48$424
35
X1=25032
FIX STAT DEG
Y1=46.55
FIX STAT DEG
Y3=15.99
FIX STAT DEG
Y5=3.35
FIX STAT DEG
ø
ø
ø
ø
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8!!!!!
"
"
""
10695
OV%t
2
8!!5I68OV
%t
0
Ý
÷
xy a b r
FIX STAT DEG
Ý
÷
xy a b r
FIX STAT DEG
Ý
÷
xy a b r
FIX STAT DEG
Ý
x' y'
FIX STAT DEG
y'(10695)
FIX STAT DEG
x'(5.68)
FIX STAT DEG
Þ
3.5143
Þ
0.0019
Þ
0.9374
24.08
1126.
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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48
Boolean Logic Operations
Press - to access a menu of Boolean Logic
operations.
Function Effect on Each Bit of the Result
AND
OR
XOR
NOT
2’s
Except for
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
Perform the operations 9 AND 2, 9 OR 2, and 9 XOR 2.
9
2
9
9
0 AND 0 = 0 0 AND 1 = 0 1 AND 1 = 1
0 OR 0 = 0 0 OR 1 = 1 1 OR 1 = 1
0 XOR 0 = 0 0 XOR 1 = 1 1 XOR 1 = 0
NOT 0 = 1 NOT 1 = 0
2’s complement
and
NOT
complement
2’s
, these functions
-
V
-"2V
-""2V
Examples
and or xor
9 and 2
9 or 2
9 xor 2
DEG
DEG
DEG
DEG
Þ
ß
0.
ß
11.
ß
11.
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48
Number-System Modes
Number system modes are second functions of keys.
%|
%~
%}
To enter the hexadecimal digits A through F, press
and then the appropriate key shown below.
Selects decimal mode (default). When the
calculator is in another number mode,
press
decimal mode.
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 return the calculator to
%|
Note
: Normally you should
%
D E F
C
B
D
A B C
F
E
G
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48
³
Problem
Add 456+125 in base 8 and in hexadecimal. Then
return the calculator to decimal mode and do the same
addition.
HEX DEG
DEG
ß
603
ß
57b
ß
581.
%~
456:125
%}#V
%|#V
V
456+125
OCT DEG
456+125
456+125
Complex Numbers
Enter a complex number as an ordered pair in
parentheses, with the real part first. Operations with
complex numbers are limited to
:, ;, <, =, 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
indicator line; press
to see the imaginary part, and
"
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
and it occupies A (for the real part) and B (for the
imaginary part); or store to C, and it occupies C and D.
, and
shows on the
r
i
,
A
41
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48
Press
%\
Returns the conjugate of a complex number.
conj
Returns the real part of a complex number.
real
Returns the imaginary part of a complex
imag
to access a menu.
number.
Returns the absolute value of a number.
abs
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.
N4%iJ2O<N3%
i5OV
"
%\
%i14OV
22
"
(4,L2)è(3,5
(4,L2)è(3,5
conj real
conj(22,14)
conj(22,14)
22.
DEG
14.
DEG
DEG
22.
DEG
M
DEG
14.
Þß
r
Þß
i
Þ
ß
r
ß
i
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48
Error Conditions
When
not accept a keyboard entry until you press
%r
appears in the display, the calculator will
Error
4
. Press
once to clear the error
4
or
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
•
•
SYNTAX
-
You attempted to divide by 0.
In statistics, n=1.
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
characters or items for Entry Line and 47 for
An entry exceeds the limit (88
-
Stat
or
Stored Operation lines).
OP
Pressing 2 or 3 when constants not defined
-
or while in
OVERFLOW
calculator:
•
•
STAT
mode.
The result is outside the range of the
-
In decimal, range |M1ä10
100
or {1ä10
100
.
In Hex, range 0-7FFFFFFFFF, 8000000001FFFFFFFFFF.
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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48
You specified an argument to a function
-
DOMAIN
outside the valid range. For example:
x
For
: 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
•
(>2
For
•
For
•
For
•
For
•
For
•
For
•
For
•
|æ| ‚ 1E10, where æ is an angle in a trig or
•
4
Rx(, P4Ry(
P
STAT
Pressing
•
When not in
•
or
%h
COMPLEX
and, or, xor
39
).
or ln: x0.
log
: x=90¡, -90¡, 270¡, -270¡, 450¡, etc.
tan
-1
or
sin
cos
-1
(x): |x|>1.
tanh
-1
(0).
cosh
-1
(x): x<0.
cosh
or
nCr
: either n or r is not an integer | 0.
nPr
function.
-
8
STAT
Using a complex number incorrectly in an
-
: x or y in Hex out of range
-1
: |x| > 1.
with no defined data points.
mode, pressing 7,
8
.
operation or in memory.
Using a base incorrectly or in the wrong mode.
-
BASE
Error in setting up integration problem:
INTEGRATE
•
•
•
-
, or
A>B
not integer 1-99, or
C
, or C undefined.
A, B
,
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48
In Case of Difficulty
Review instructions to be certain calculations were
performed properly.
Press
and
T
released, memory and settings are cleared, and
MEM CLEARED
Check the battery to ensure that it is fresh and properly
installed.
Change the battery when:
does not turn the unit on, or
• T
The screen goes blank, or
•
You get unexpected results.
•
simultaneously to reset. When
4
is displayed.
Battery Replacement
Replace protective cover. Place the TI-36X
down.
1. Remove screw case, using a small Phillips
screwdriver.
2. Carefully separate front from back, starting from the
3. Remove battery, using a small Phillips screwdriver,
4. If necessary, press
5. Properly dispose of used batteries immediately. Do
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48
Caution
bottom.
internal parts.
if necessary; replace with new battery. Install
batteries according to polarity (+ and -) diagrams.
Caution
components while changing the battery.
to reset. When released, memory and settings are
cleared, and
not leave them within the reach of children.
: Be careful not to damage any
: Avoid contact with other TI-36X
and
T
4
MEM CLEARED
is displayed.
45
face
ü
ü
simultaneously
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:
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.
ti-cares@ti.com
education.ti.com
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