n
Other functions ( x
– 1
,
,
X
,x
2
,
∧
)
• The calculator also provides reciprocal ( [ x
–1
] ), square root
( [
] ), universal root [
X
], square ( [ x
2
] ) and exponentia-
tion ( [
∧
] ) functions. See Example 47~50.
n
Unit Conver sion
• The calculators has a built-in unit conversion feature that enables
you to convert numbers from metric to English units and vice versa.
See Example 51.
1. Enter the number you want to convert.
2. Press [ 2nd ] [ CONV ] to display the menu. There are 7
menus, covering distance, area, temperature, capacity, weight,
energy, and pressure.
3. Use the [
6
] [
5
] to scroll through the list of units until a appro-
priate units menu is shown, then [
].
4. Pressing [
4
] or [
3
] can convert the number to another unit.
n
Phy si cs co nstant s
• You can use a number physics constants in your calculations. W ith
the following constants :
Symbol
Meaning
Value
c
Speed of light
299792458 m / s
g
Acceleration of gravity 9.80665 m.s
– 2
G
Gravitational constant
6.6725985 x 10
– 11
N.m
2
kg
–2
Vm
molar volume of ideal gas 0.0224141 m
3
mol
– 1
NA
Avagadro’s number
6.022136736 x 10
23
mol
– 1
e
Elementary charge
1.602177335 x 10
–19
C
me
Electron mass
9.109389754 x 10
–31
kg
mp
Proton mass
1.67262311 x 10
–27
kg
h
Plank’s constant
6.62607554 x 10
–34
J.s
k
Boltzmann’s constant
1.38065812 x 10
–23
J.K
–1
R
Gas constant
8.3145107 J / mol • k
F
Faraday constant
96485.30929
C / mol
mn
Neutron constant
1.67492861 x 10
–27
kg
µ
Atomic mass constant
1.66054021 x 10
–27
kg
0
ε
Dielectric perm ittivity
8.854187818 x 10
–12
F / m
0
µ
Magnetic permittivity
0.000001257
H / m
0
ϕ
Flux quantum
2.067834616 x 10
–15
Vs
0
a
Bohr radius
5.2917724924 x 10
–11
m
µ
B
Bohr magneton
9.274015431 x 10
–24
A • m
2
µ
N
Neutron magnetic moment 5.050786617 x 10
–27
J / T
To insert a constant at the cursor position ( See Example 52. ) :
1. Press [ CONST ] to display the physics constants menu.
2. Press [
4
] until the constant you want is underlined.
3. Press [
].
Mode 1 - STAT
There are three menu operation in statistics m enu :
1 -VAR
( for
analyzing data in a single dataset),
2 - VAR
( for analyzing paired data
from two datasets ) and
D- CL
( for clearing all datasets).
n
Single-Variable / Two-variable statistics
Step :
1. From the statistics menu, choose
1 -VAR
or
2 - VAR
and press
[
].
2. Press [ DATA ] and there are three menu :
DATA-INPUT
,
LIMIT-
SET
,
DISTR
. Please choose
DATA-INPUT
and press [
].
3. Enter an x - value and press [
6
].
4. Enter the frequency (
FREQ
) of the x - value (in
1 -VAR
mode)
or the corresponding y - value ( in
2 - VAR
mode ) and press
[
6
].
5. To enter more data, repeat from step 3.
6. Press [ STATVAR ] and scroll through the statistical results
menu by [
4
] or [
3
] to find out statistical variables you want.
(See table below)
Variable
Meaning
n
Num ber of the x values or x-y pairs entered.
_
_
x
or
y
Mean of the x values or y values
Xmax
or
Ymax
Maximum of the x values or y values
Xmin
or
Ymin
Minimum of the x values or y values
Sx
or
Sy
Sample standard deviation of x values or y
values.
1
n
)
x
x
(
x
S
2
−
−
∑
=
,
1
n
)
y
y
(
y
S
2
−
−
∑
=
σ
x
or
σ
y
Population standard deviation of x values or y
values
n
)
x
x
(
2
x
−
∑
=
σ
,
n
)
y
y
(
2
y
−
∑
=
σ
Σ
x
or
Σ
y
Sum of all x values or y values
Σ
x
2
or
Σ
y
2
Sum of all x
2
values or y
2
values
Σ
x y
Sum of (x x y) for all x-y pairs
n
Pro cess cap abil ity
Step : (See Example 53~54)
1. Press [ DATA ] and there are three menu :
DATA- INPUT
,
LIMIT-
SET
,
DISTR
. Please choose
LIMIT-SET
and press [
].
2. Enter a upper spec. limit value (
X USL
or
Y USL
), then press
[
6
].
3. Enter a lower spec. limit value (
X LSL
or
Y LSL
), then press
[
].
4. Enter the datasets you want under
DATA-INPUT
mode.
5. Press [ STATVAR ] and scroll through the statistical results
menu by [
4
] or [
3
] to find out process capability variables you
want. (See table below)
Variable
Meaning
Cax
or
Cay
Capability accuracy of the x values or y values
,
Cpx
or
Cpy
Potential capability precision of the x values or y values,
,
Cpkx
or
Cpky
Minimum (C
PU
, C
PL
) of the x values or y
values, where C
PU
is upper spec. limit of
capability precision and C
PL
is lower spec.
limit of capability precision
C
pkx
= Min (C
PUX
, C
PLX
) = C
px
(1– C
ax
)
C
pky
= Min (C
PUY
, C
PLY
) = C
py
(1– C
ay
)
(Note): W hen calculating process capability in
2 - VAR
mode,
the x
n
and y
n
are independent with each other.
n
Pro babili ty distribut ion
Step : (See Example 55)
1. Based on the datasets in 1-VAR mode, press [ DATA ] and
there are three menu :
DATA-INPUT
,
LIMIT-SET
,
DISTR
. Please
choose
DISTR
and press [
].
2. Enter a
a
x
value, then press [
].
3. Press [ STATVAR ] and scroll through the statistical results
menu by [
4
] or [
3
] to find out probability distribution vari-
ables you want. (See table below)
Variable
Meaning
t
Test value
P(t)
Represent the cum ulative fraction of the stan-
dard norm al distribution that is less than the
value t
R (t)
Represent the cum ulative fraction of the stan-
dard normal distribution that lies between the
value t and 0.
R(t)=1– P(t)
Q(t)
Represent the cum ulative fraction of the stan-
dard normal distribution that is greater than the
value t
Q(t)=| 0.5–R(t) |
n
L i n ear r e g r essi o n
Step : (See Example 56)
1. Based on the datasets in
2 - VAR
mode, press [ STATVAR ] and
scroll through the statistical results menu by [
4
] or [
3
] to
find out
a
,
b
, or
r
.
2. To predict a value for x (or y) given a value for y (or x), select
the
x ’
(or
y ’
) variable, press [
], enter the given value, and
press [
] again. (See table below)
Variable
Meaning
a
Linear regression y-intercept
n
x
b
y
a
∑
∑
−
=
b
Linear regression slope
)
)
x
(
x
n
(
)
y
x
xy
n
(
b
2
2
∑
−
∑
∑
∑ ∑
−
=
r
Correlation coefficient
)
)
y
(
y
n
)(
)
x
(
x
n
(
)
y
x
xy
n
(
r
2
2
2
2
∑
−
∑
∑
−
∑
∑
∑ ∑
−
=
x ’
Predicted x values given a, b, and y vales
b
a
–
y
'
x
=
y ’
Predicted y value given a, b, and x value.
bx
a
'
y
+
=
n
Co rrectin g data
Step : (See Example 57)
1. Press [ DATA ].
2. To change x - values or the frequency of the x - value in
1 - VAR
mode ( or the corresponding y - value in
2 - VAR
mode ), please
choose
DATA-INPUT
. To change upper spec. limit value, or
lower spec. limit value, please choose
LIMIT-SET
. To change
a
x
, please choose
DISTR
.
3. Press [
6
] to scroll through the data you have entered.
4. To change an entry, display it and enter the new data. The new
data you enter overw rites the old entry. Pre ss [
6
] or
[
] to save the change.
(Note) : Even you exit STAT mode, all data in
1 - VAR
and
2 - VAR
mode
are still retained unless you clear all data by selecting
D-
CL
mode.
Mode 2 - Base-n
n
Bases co n v ersi o ns
• The number system (10, 16, 2 , 8 ) is set by pressing [ 2nd ] [ dhbo ]
to display the menu, making one of the items underlined followed
[
]. A corresponding symbol - “
d
”, “
h
”, “
b
”, “
o
” appears on
the display. (The default setting is
d
: decimal base). See Example
58.
(Note) : The total range of numbers handled in this mode is 0, 1, 2,
3, 4, 5, 6, 7, 8, 9, /A, IB, IC, ID, IE, IF. If values not valid for
the particular number system are used, attach the corre-
sponding designator (
d
,
h
,
b
,
o
), or an error message will
appear.
Binary base (
b
) : 0, 1
Octal base (
o
) : 0, 1, 2, 3, 4, 5, 6, 7
Decimal base (
d
) : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Hexadecimal base (
h
) : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /A, IB, IC,
ID, IE, IF
• Pressing [
] can use block function to display a result in octal or
binary base w hich exceeds 8 digits. The system is designed to
display up to 4 blocks. See Example 59.
n
Neg ati v e expr essi on s
• In binary, octal, and hexadecimal bases, the calculator represents
negative numbers using complement notation. The complement is
the result of subtracting that num ber from 10000000000 in that
number’s base by pressing [ NEG ] key in non-decimal bases. See
Example 60.
n
Basi c ari th met ic op er at ions for b ases
• The unit enables you to calculate in number base other than decimal.
The calculator can add, subtract, multiply, and divide binary, octal,
and hexadecimal numbers. See Example 61.
n
Lo gical o per ati on
• Logical operations are performed through logical products (AND),
negative logical (NAND), logical sum s (OR), exclusive logical
sums (XOR), negation (NOT), and negation of exclusive logical
sums (XNOR). See Example 62.
Mode 3 - CPLX
• Complex mode enables you to add, subtract, multiply, and divide
complex numbers. See Example 63. The results of a complex op-
eration are displayed as follow :
Re
Real value
Im
Imaginary value
ab
Absolute value
ar
Argument value
Mode 4 - VLE
Variable linear equations (
VLE
) mode can solve a set of
simultaneous equations with two unknowns as follows :
a x + b y = c
d x + e y = f, where x and y are unknown.
• In VLE mode, you just enter each coefficient (
a
,
b
,
c
,
d
,
e
,
f
) in the
correct order, and the calculator automatically solves for
x
,
y
. See
Example 64.
Mode 5 - QE
Quadratic equations (
QE
) mode can solve a equations as follows :
a x
2
+ b x + c = 0, where x is unknown.
• In QE mode, you just enter each coefficient (
a
,
b
,
c
) in the correct
order, and the calculator automatically solves for all
x
values. See
Example 65.
• Num ber display formats are selected by pressing [ 2nd ] [ SCI/
ENG ] to display the menu. The items on the menu are
FLO
(for
floating point),
SCI
(for scientific), and
ENG
(for engineering).
Press [
3
] or [
4
] until the desired formats is underlined, and then
press [
]. See Example 13.
(Note) :The engineering format is similar to the scientific format,
except the mantissa can have up to three digits left of the
decimal, instead of only one, and the exponent is always a
multiple of three. It is useful for engineers to convert units
based on multiples of 10
3
.
• You can enter a number in mantissa and exponent form by [ EXP ]
key. See Example 14.
n
Par ent h eses cal cu l at i on s
• Operation inside parentheses are always executed first.
AT-36
can use up to 13 levels of consecutive parentheses in a single
calculation. See Example 15.
• Closed parentheses occurring immediately before operation of the
[
] key may be omitted, no matter how many are required. See
Example 16.
• A multiplication sign “ x ” occurring immediately before an open
parenthesis can omitted. See Example 17.
(Note) :The calculator can auto-correct abbreviated multiplica-
tion in front of all functions, except memory variables, left
parenthesis, type B functions.
• Henceforth, abbreviated type will not be used in this manual. See
Example 18.
• The correct result cannot be derived by entering [ ( ] 2 [ + ] 3 [ ) ]
[ EXP ] 2. Be sure to enter [ x ] 1 between the [ ) ] and [ EXP ] in
the below example. See Example 19.
n
Percent age calculati on
• [ 2nd ] [ % ] divides the number in the display by 100. You can use
this key sequence to calculate percentages, add-ons, discounts,
and percentages ratios. See Example 20~21.
n
Contin uous calcu lation fun ction
• The calculator enables you to repeat the last operation executed by
pressing [
] key for further calculation. See Example 22.
• Even if calculations are concluded with the [
] key, the result
obtained can be used for further calculation. See Example 23.
n
An swer f u n ct i o n
• Answer function stores the most recently calculated result. It is
retained even after the power is turned off. Once a numeric value
or numeric expression is entered and [
] is pressed, the result
is stored by this function. See Example 24.
(Note) :Even if execution of a calculation results in an error,
however, Answer memory retains its current value.
n
L og ar it h ms and An ti lo g ar it hms
• The calculator can calculate common and natural logarithms and
anti-logarithms using [ LOG ], [ LN ], [ 2nd ] [ 10
x
], and [ 2nd ]
[ e
x
]. See Example 25~27.
n
Fraction calculation
Fraction value display is as follow :
• To enter a mixed num ber, enter the integer part, press [ A
b
/
c
],
enter the numerator, press [ A
b
/
c
], and enter the denominator ; To
enter an improper fraction, enter the numerator, press [ A
b
/
c
], and
enter the denominator. See Example 28.
• During a fraction calculation, if the figure is reducible, a figure is
reduced to the lowest terms after pressing a function command key
( [ + ], [ – ], [ x ] or [ ] ) or the [
] key. By pressing [ 2nd ]
[ A
b
/
c
34
d
/
e
], the displayed value will be converted to the improper
fraction and vice versa. See Example 29.
• To convert between a decimal and fractional result, press [ 2nd ]
[ F
34
D ] and [
]. See Exam ple 30.
• Calculations containing both fractions and decimals are calcu-
lated in decimal format. See Example 31.
n
Ang le u ni ts con versio n
• The angle units (
DEG
,
RAD
,
GRAD
) is set by pressing [ DRG ] to
display the angle menu. The relation among the three angle units
is :
180 ° =
π
rad = 200 grad
Angle conversions ( See Example 32.) :
1. Change the default angle settings to the units you want
to convert to.
2. Enter the value of the unit to convert.
3. Press [ DMS ] to display the menu. The units you can
select are
°
(degrees),
′
(minutes),
′′
(seconds),
r
(radians),
g
(gradians) or
4
DMS
(Degree-Minutes-
Seconds).
4. Choose the units you are converting from.
5. Press [
] twice.
• To convert an angle to DMS notation, select
“
4
DMS
”, which con-
verts an entry to DMS notations, i.e., where
1
O
30
I
0
II
represents
1 degrees, 30 minutes, 0 seconds. See Example 33.
• To convert a DMS notation to decimal, select
°
(degrees),
′
(minutes),
′′
(seconds). See Example 34.
n
Tr igo nometr ic / I nver se- Tri . f unctio ns
•
AT-36 provides standard trigonometric functions and inverse
trigonometric functions - sin, cos, tan, sin
–1
, cos
–1
and tan
–1
. See
Example 35~37.
(Note) :W hen using those keys, make sure the calculator is set for
the angle unit you want.
n
Hyperbolic / Inver se-Hyp . funct ions
•
AT-36 uses [ 2nd ] [ HYP ] to calculate the hyperbolic functions
and inverse- hyperbolic functions - sinh, cosh, tanh, sinh
–1
,
cosh
–1
and tanh
–1
. See Example 38~39.
(Note) :W hen using those keys, make sure the calculator is set for
the angle unit you want.
n
C oo r d in ates tr an sf o rmat io n
• Pressing [ 2nd ] [ R
34
P ] displays a menu to convert rectangular
coordinates to polar coordinates or vice versa. See Example
40~41.
Rectangular Coordinates
Polar Coordinates
x + y i= r (cos
θ
+ i sin
θ
)
(Note) :W hen using those key, make sure the calculator is set for
the angle unit you want.
n
Probab ility
• Pressing [ PRB ] displays the probability menu. See Example 42~46.
W ith the following functions :
n Pr
Calculates the number of possible permutations of n item
taken r at a time.
n C r
Calculates the number of possible combinations of n items
taken r at a time.
!
Calculates the factorial of a specified positive integer n
, where n
≦
69.
RANDM
Generates a random number between 0 and 1.
RANDMI
Generates a random integer value between two specified
integers, A and B, where A
≦
random value
≦
B .
5
/
12 Display of
12
5
56
∪
5
/
12 Display of 56 12
5
Y
X
0
• P( x, y )
x
y
• P( r,
θ
)
0
X
θ
r
Y
