hp 9s
Trigonometric and Inverse Trigonometric Functions
Before undertaking a trigonometric or inverse trigonometric
calculation, make sure that the appropriate angular unit is set.
Ex. 7: Change 12385 to 789
1. Key in 12385
Mixed Arithmetic Calculations
DEG
DEG
Scientific Calculator
789.
123.
DEG
DEG
ENTER
1 [ + ] 2 [ × ] 3 [ ]
1 + 2 × 3 = ?
7.
2. Press [ CE ] 789
DEG
ENTER
]
3 sin 85° = ?
3 [ × ] 85 [ sin ] [
π
2.99
0.71
÷
3.5 [ +/– ] [ + ] 8 [
] 2
0.5
÷
–3.5 + 8 2 = ?
π
4
Ex. 8: Change 12385 to 123
1. Key in 12385
÷
ENTER
] 4 [ ]
[ 2ndF ] [
[ cos ]
] [
ENTER
[
]
RAD
General Operations
cos (
rad) = ?
Parentheses Calculations
Operations inside parentheses are always executed first. You can
specify up to 15 levels of parentheses in a single calculation. When
you enter the first parenthesis, the ( ) indicator appears on the display
and remains until each opening parenthesis has a corresponding
closing parenthesis.
Power Supply
On or Off
GRAD
DEG
tan 150 grad = ?
150 [ tan ]
–1.00
30.00
→
2. Press [ 00 0 ] twice.
sin –1 0.5 = ? deg 0.5 [ 2ndF ] [ sin –1
]
To turn the calculator on, press [ON/C].
In a series of calculations, you can correct errors in intermediate
results by pressing [ON/C]. This clears the calculation without clearing
memory.
1
cos –1
? rad
(
) =
√
[ cos –1
2 [
] [ 2ndF ] [ x –1] [ 2ndF ]
]
RAD
To turn the calculator off, press [2ndF] [OFF].
0.79
2
Auto power-off function
If you press the wrong arithmetic operation key, just press [ CE ] and
then the correct arithmetic key.
tan –1 1 = ? grad
1 [ 2ndF ] [ tan –1
]
GRAD
The calculator automatically turns off if it has not been used for
approximately 9 minutes. Power can be restored by pressing the
[ON/C] key again. Memory contents and the current mode setting
(STAT, DEG, CPLX, Base-n,etc) are retained when you turn off the
power and when the calculator automatically turns off.
50.00
DEG
( 5 – 2 × 1.5 ) ×
3 + 0.8 × (– 4 )
= ?
2.8
[ ( ] 5 [ – ] 2 [ × ] 1.5 [ ) ] [ × ] 3
ENTER
Exchange key
Hyperbolic and Inverse hyperbolic functions
[ + ] 0.8 [ × ] 4 [ +/– ] [
]
←→
Pressing [ 2ndF ] [ X Y ] changes the currently displayed value to
the previously displayed value.
cosh1.5+sinh1.5
= ?
1.5 [ HYP ] [ cos ] [ + ] 1.5
ENTER
DEG
DEG
2 × ( 7 + 6 × ( 5 2 [ × ] [ ( ] 7 [ + ] 6 [ × ] [ ( ] 5
ENTER
4.48
122.
[ HYP ] [ sin ] [
]
+ 4 )) = ?
[ + ] 4 [
]
sinh –1 7 = ?
tanh 1 =?
7 [ HYP ] [ 2ndF ] [ sin –1
]
DEG
DEG
DEG
2.64
0.76
Battery replacement
ENTER
]
123 [ + ] 456 [
579.00
456.00
579.00
ENTER
].
Note: It is not necessary to press [ ) ] before [
DEG
DEG
1 [ HYP ] [ tan ]
←→
[ 2ndF ] [ X Y ]
123 + 456 = ?
The calculator is powered by two alkaline button batteries (GP76A or
LR44). If the display becomes dim and difficult to read, the batteries
should be replaced as soon as possible.
Repeating a Calculation
←→
[ 2ndF ] [ X Y ]
Rectangular and Polar coordinates
You can repeat the last number entered, or the last operation
ENTER
Rectangular Coordinates
Polar Coordinates
Accuracy and Capacity
Accuracy: ±1 in the 10th digit.
executed, by pressing [
].
To replace the batteries:
Repeating the last number
1. Slide the battery cover off and remove the old batteries.
2. Insert new batteries, with positive polarity facing outward.
3. Replace the battery cover and press [ON/C] to turn on the power.
DEG
DEG
DEG
Capacity: In general, calculations can be displayed as a mantissa of
up to 10 digits, a 10-digit mantissa together with a 2-digit exponent up
to 10 ±99, or as an integer between –9999999999 and 9999999999.
ENTER
3 [ × ] [
]
9.
27.
81.
3 × 3 = ?
3 × 3 × 3 = ?
ENTER
[
[
]
3 × 3 × 3 × 3 = ?
ENTER
]
Numbers used as input to a particular function must be within the
allowable range for that function (as set out in the following table):
The keyboard
Repeating the last arithmetic operation
Most of the keys can perform two functions.
DEG
DEG
ENTER
321 [ + ] 357 [
321 + 357 = ?
654 + 357 = ?
]
678.
ENTER
654 [
]
Functions
Allowable input range
< 4.5 × 10 10 deg
< 2.5 × 10 8 π rad
< 5 × 10 10 grad
1011.
2nd function
sin–1
sin
sin x, cos x, tan x
――――――
Deg:
Rad:
Grad:
x
x
DEG
DEG
a + b i = r (cosθ + i sinθ)
ENTER
]
579 – 159 = ?
456 – 159 = ?
579 [ – ] 159 [
ENTER
420.
297.
―――
1st function
Note: Before undertaking a coordinates conversion calculation, make
sure that the appropriate angular unit is set.
456 [
]
1st functions
x
DEG
DEG
DEG
ENTER
3 [ × ] 6 [ × ] 45 [
]
810.
414.
900.
18 × 45 = ?
18 × 23 = ?
These are functions that are executed when you press a key without
first pressing [ 2ndF ]. The function performed is indicated by the label
on the key.
Converting from Rectangular to Polar
Also, for tan x:
ENTER
23 [
]
DEG
→
5 [ a ] 6 [ b ] [ 2ndF ] [ R P ]
If a = 5 and b = 6,
18 × (0.5x102) = ?
7.81
Deg:
Rad:
x
x
≠ 90 (2n +1)
ENTER
0.5 [ EXP ] 2 [
]
DEG
θ
?
what are r and
[ b ]
50.19
π
2
2nd functions
≠
(2n +1)
DEG
DEG
DEG
÷
÷
÷
ENTER
]
Converting from Polar to Rectangular
96
75
8 = ?
8 = ?
96 [
75 [
] 8 [
12.
9.375
15.
These are functions that are executed when you press a key after first
pressing [ 2ndF ]. The function performed is indicated by the label
above the key.
ENTER
25 [ a ] 56 [ b ] [ 2ndF ]
→
[ P R ]
]
θ
Grad:
x
≠ 100 (2n +1)
If r = 25 and
=
DEG
DEG
13.98
20.73
(1.2x102)
8 = ?
÷
56°, what are a
ENTER
1.2 [ EXP ] 2 [
]
where n is an integer.
and b?
[ b ]
When you press [ 2ndF ], the 2ndF indicator appears in the display to
indicate that you will be selecting the second function of the next key
you press. If you press [ 2ndF ] by mistake, simply press [ 2ndF ]
again to remove the 2ndF indicator.
sin –1 x, cos –1
tan –1
x
Percentage Calculations
x
x
x
x
x
≦ 1
Permutations and Combinations
120 [ × ] 30 [ 2ndF ] [ % ]
ENTER
DEG
DEG
DEG
< 1 × 10 100
≦ 230.2585092
< 1 × 10 100
< 5 × 10 99
30% of 120 = ?
70% of 120 = ?
36.
84.
[
]
x
n!
n!
nPr =
nCr =
ENTER
70 [ 2ndF ] [ % ] [
]
(n− r)!
r !(n − r)!
Note: [ A ], [ B ], [ C ], [ D ], [ E ], [ F ] are 1st functions in HEX mode.
sinh x, cosh x
tanh x
÷
88 is 55% of what 88 [
] 55 [ 2ndF ] [ % ]
How many
160.
number?
ENTER
]
Display Symbols
[
permutations of 4
items can you
select from a set
of 7 items?
DEG
DEG
ENTER
]
30% mark up of
120 = ?
120 [ + ] 30 [ 2ndF ] [ % ]
ENTER
7 [ 2ndF ] [ nPr ] 4 [
7 [ 2ndF ] [ nCr ] 4 [
DEG
DEG
840.00
35.00
The following symbols, shown on the display, indicate the status of
the calculator.
156.
84.
sinh –1
x
[
]
30% discount of
120 = ?
120 [ – ] 30 [ 2ndF ] [ % ]
ENTER
cosh –1
tanh –1
x
1 ≦ x < 5 × 10 99
< 1
[
]
How many
DEG or RAD or GRAD: degrees, radians or grads angular unit
combinations of 4
items can you
select from a set
of 7 items?
Memory Calculations
x
M
E
A value is in memory
Overflow or error
Minus
CPLX Complex number mode
x
ENTER
]
The M indicator appears when a number is stored in memory.
Recalling from memory does not delete the contents of memory.
The memory is not available when you are in statistics mode.
•
•
•
•
STAT Statistical mode
log x, ln x
1 × 10 –99 ≦ x < 1 x 10 100
–1 × 10 100 ＜ x ＜ 100
–1 × 10 100 ＜ x ≦ 230.2585092
0 ≦ x < 1 × 10 100
–
2ndF
[2ndF] key pressed
Precision capability
Process capability
Deviation
( )
Parentheses calculation CP
10 x
e x
↔
Sexagesimal
You can convert a sexagesimal figure (degree, minute and second) to
a decimal number by pressing [ ] and convert a decimal number
Decimal form Conversions
BIN Binary mode
OCT Octal mode
CPK
σ
→
To copy the displayed number to memory, press [ X M ].
x
→
→
To clear the memory, press [ 0 ] [ X M ], or [ CE ] [ X M ], in
that order.
•
to a sexagesimal figure by pressing [ 2ndF ] [
].
HEX Hexadecimal mode
USL
LSL
Setting upper limit
Setting lower limit
x 2
x –1
x
< 1 × 10 50
│x│＜1 × 10 100, X≠0
< 1 × 10 100
Sexagesimal figures are displayed as follows:
ED
Edit mode
HYP Hyperbolic mode
12 ꢀ 45
׀ 30 ׀ ׀ 5
= 12 degrees, 45 minutes, 30.5
seconds
DEG
→
[ CE ] [ X M ]
0.
15.
8.
DEG
DEG
DEG
DEG
DEG
3
3 [ × ] 5 [ M+ ]
x
x
M
M
M
M
Note: If the total number of digits in a DD, MM and SS.SS figure
exceeds 8, the figure is truncated.
3 × 5
Display Formats
÷
56 [
] 7 [ M+ ]
÷
+ 56
7
≦
≦
0
x
69, where x is an integer.
The calculator can display numbers in four formats: floating point,
fixed point, scientific, and engineering.
X !
+ 74 – 8 × 7
Total = ?
74 [ – ] 8 [ × ] 7 [ M+ ]
[ MR ]
→
18.
41.
0.
Converting from Sexagesimal to Decimal
1 × 10 100
1 × 10 100
→
R
P
2
2
＜
x
+ y
12 deg., 45 min.,
30.5 sec.= ?
12 [
[
] 45 [
] 30.5
DEG
DEG
Floating point format
12.76
]
→
P
≦
＜
r
R
0
0 [ X M ]
The floating point format displays numbers in decimal form, using up
to 10 digits. Any trailing zeros are truncated.
Deg
Rad
Grad
4.5 × 10 10 deg
Converting from Decimal to Sexagesimal
2.12345 = ? 2.12345 [ 2ndF ] [
：│θ│＜
Common Math Calculations
The following example calculations assume that your display is fixed
at 2 decimal places.
2 ꢀ 7
׀ 24 ׀׀ 42 ：│θ│＜
8π
]
2.5 × 10
rad
If the result of a calculation is too large to be represented by 10 digits,
the display automatically switches to scientific format. If the result of a
later calculation is small enough to be displayed in less than 10 digits,
the calculator returns to floating point format.
5 × 10 10 grad
：│θ│＜
Base-n Calculations
Converting between bases
Also, for tan x:
Reciprocal, Factorial
：│θ│≠
Deg
Rad
Grad
90 (2n+1)
1
You can add, subtract, multiply, and divide binary, octal, and
hexadecimal numbers in addition to decimal numbers. Select the
1.25 [ 2ndF ] [ x –1] [
DEG
ENTER
]
To set the display to floating point display format:
= ?
0.80
π
1.25
：│θ│≠
(2n+1)
2
DEG
DEG
•
0.
→
→
→
4. Press [ 2ndF ] [ FIX ] [
]
number base you want by pressing [ BIN], [ OCT], [ HEX], or
ENTER
]
5! = ?
5 [ 2ndF ] [ x! ] [
120.00
→
DEC]. The BIN, OCT, and HEX indicators show you which base
：│θ│≠
[
100 (2n+1)
Fixed point format
Square, Square Root, Cube Root, Power, Other Roots
you are using. (If none of these indicators is displayed, you are using
decimal base.)
2 2 + 3 4 = ?
2 [ x 2 ] [ + ] 3 [ x y ] 4 [
5 [ × ] 27 [ 2ndF ] [ 3 ] [ + ]
where n is an integer.
│DD│, MM, SS.SS ＜ 1 × 10 100
DEG
ENTER
]
The fixed point, scientific, and engineering formats use a fixed
number of decimal places to display numbers. If more than the
specified number of decimal places is keyed, the entry will be rounded
to the correct number of decimal places.
85.00
20.83
1.61
,
√
DEG
DEG
5 ×3
+
= ?
34
The number keys that are active in a particular base are:
Binary base: [ 0 ] and [ 1 ]
27
√
ENTER
]
34 [
] [
0 ≦ MM, SS.SS
72 [ 2ndF ] [ X ] 9 [
9
= ?
√
ENTER
]
72
x
< 1 × 10 100
Octal base: [ 0 ] to [ 7 ]
Ex. 1: Fix the display at 2 decimal places, then key in 3.256
Logarithms and Antilogarithms
x y
x > 0 : –1 × 10100 < y log x < 100
DEG
Decimal base: [ 0 ] to [ 9 ]
1. Press [ 2ndF ] [ FIX ] 2
ENTER
0.00
3.26
DEG
DEG
ENTER
7 [ ln ] [ + ] 100 [ log ] [
2 [ 2ndF ] [ 10 x ] [
ln7 + log100 = ?
10 2 = ?
]
3.95
Hexadecimal base: [ 0 ] to [ 9 ] and [ A ] to [ F ]
x = 0 : y > 0
DEG
ENTER
]
2. Key in 3.256 [
]
100.00
DEG
→
[ 2ndF ] [ DEC] 31
5 [ 2ndF ] [ e x ] [ – ] 2 [+/–]
ENTER
31.
11111.
37.
x < 0 : y = n, 1/(2n+1)
31 (base 10)
= ? (base 2)
= ? (base 8)
e 5 – e –2 = ?
DEG
If fewer than the set number of decimal places is keyed, the entry will
be padded with trailing zeros.
DEG BIN
DEG OCT
DEG HEX
[ 2ndF ] [ e x ] [
]
148.28
→
[ 2ndF ] [ BIN]
→
where n is an integer
[ 2ndF ] [ OCT]
→
but –1 x 10100
<
log x 100
1
y
Ex. 2: Fix the display at 4 decimal places, then key in 4.23
Fraction calculations
Fractions are displayed as follows:
= ? (base 16)
[ 2ndF ] [ HEX]
→
1F.
DEG
1. Press [ 2ndF ] [ FIX ] 4
0.0000
4.2300
[ 2ndF ] [ HEX] 4 [ × ] 1B
ENTER
x Y
DEG HEX
DEG
1
y > 0 : x ≠ 0, –1 x 10100
<
log y < 100
6C.
4 × 1B (base 16)
= ? (base 2)
DEG
[
]
ENTER
x
2. Key in 4.23 [
]
BIN1101100.
108.00
5
→
[ 2ndF ] [ BIN]
→
」
」
5
12
=
=
y = 0 : x > 0
Scientific format
= ? (base 10)
= ? (base 8)
12
DEG
[ 2ndF ] [ DEC]
→
In scientific format, the number 891500 is shown as 8.915 × 10 05
where 8.915 is the mantissa and 5 is the exponent of 10.
,
y < 0 : x =2n+1, l/n
DEG OCT
[ 2ndF ] [ OCT]
154.
5
∪
56
5
12
where n is an integer other than 0
but –1 x 10100
56
12
Negative Numbers and Complements
Ex. 3: To display 7132 × 125 in scientific format:
1
<
log y 100
Note : The display is truncated if the integer, numerator, denominator
and fraction symbols together are more than 10 digits.
DEG
x
In binary, octal, and hexadecimal bases, negative numbers are
expressed as complements. The complement is the result of
subtracting that number from 10000000000 in that number’s base.
You do this by pressing [+/–] in a non-decimal base.
ENTER
1. Key in 7132 [ × ] 125 [
]
891500.
8.915
b
Input：The integer, numerator, denominator
and fraction symbols must in total be no
more than 10 digits.
a
/c
DEG
05
d
→
←→
2. Press [ F E ]
Press [ 2ndF ] [
fraction.
/c ] to convert the displayed value to an improper
You can convert an entry to scientific notation by pressing [EXP] after
entering the mantissa.
Ex. 4: Key the number 4.82296 × 10 5
Result：Displayed as a fraction when the
Calculate the
complement of
binary number
11011
2
3
3
5
DEG BIN
integer, numerator and denominator are
b
b
+ 7
4
2 [ a /c ] 3 [ + ] 7 [ a /c ] 3
b
DEG
DEG
→
[ 2ndF ] [ BIN ] 11011 [+/–]
each less than 1 × 1010
.
∪
」
15
8
4
1111100101.
ENTER
[ a /c ] 5 [
]
DEG
05
0 ≦r≦n, n≦9999999999; n, r are integers.
nPr, nCr
STAT
1. Key in 4.82296 [ EXP ] 5
4.82296
= 8
15
x < 1 × 10 50 , Σ x < 1 × 10 100
Complex Number Calculations
Engineering format
124
0 ≦│Σx 2│＜1 × 10 100; n, r are integer
=
d
→
[ 2ndF ] [
/c ]
」
124 15
Press [ CPLX ] to enter complex number mode. The CPLX indicator
appears on the display. You can add, subtract, multiply, and divide
complex numbers.
15
Engineering format is similar to scientific format, except that the
：n≠0, S：n＞1,σ：n＞0
x
mantissa can have up to three digits to the left of the decimal and the
exponent is always a multiple of three. This is useful if you have to
b
ENTER
], or if a fraction was
If you press [ a /c ] after pressing [
Range = 1 ~ r, 1≦n≦r, 80≦r≦20400
0 ≦ X ≦9999999999 (for zero or positive)
–9999999999 ≦ X ≦ –1 (for negative)
combined with a decimal number, the answer is displayed as a
decimal number.
convert units that are based on multiples of 10 3
Ex. 5: Convert 15V to 15000mV (V = Volts)
.
Complex numbers are generally represented as a + b i, where a is the
real part and bi is the imaginary part.
→DEC
4
9
3
4
b
b
5 [ a /c ] 4 [ a /c ] 9 [ + ] 3
DEG
[ 2ndF ] [ CPLX ] 7 [ a ] 9
DEG
5
+ 3
∪
」
9
7
36
9.19
12.19
1. Key in 15
15.
≦
≦
DEG CPLX
0
X
0111111111 (for zero or
→BIN
b
b
ENTER
[ a /c ] 3 [ a /c ] 4 [
]
[ +/– ] [ b ] [ + ] 15 [ a ] 10 [ b ]
ENTER
( 7 – 9 i ) +
(15 + 10 i) = ?
22.00
1.00
positive)
7
DEG
– 03
[
]
DEG
DEG
2. Press [ ENG ] twice.
Ex. 6: Convert 15V to 0.015KV (V = Volts)
1. Key in 15
15000.
= 9
= 9.19
b
DEG CPLX
[ a /c ]
36
[ b ]
1000000000 ≦ X ≦ 1111111111
(for negative)
b
b
4
8
8 [ a /c ] 4 [ a /c ] 9 [ + ]
Note: Memory calculation is available in complex number mode.
+ 3.75 = 12.19
DEG
DEG
ENTER
3.75 [
]
9
15.
→OCT
0 ≦ X ≦ 3777777777 (for zero or positive)
4000000000 ≦ X ≦ 7777777777
(for negative)
Random Numbers
Press [ 2ndF ] [ RND ] to generate a random number between 0.000
and 0.999.
Where possible, a fraction is reduced to its lowest terms after you
ENTER
03
←
←
0.015
2. Press [ 2ndF ] [
] [ 2ndF ] [
]
÷
press [ + ], [ – ], [ × ], [
] or [
].
Order of Operations
b
b
3 [ a /c ] 119 [ a /c ] 21
ENTER
119
21
2
3
DEG
∪
」
8
2
3
Unit Conversions
3
= 8
[
]
Each calculation is performed in the following order of precedence:
1. Operations in parentheses.
→HEX
0 ≦ X ≦2540BE3FF (for zero or positive)
FDABF41C01 ≦ X ≦ FFFFFFFFFF (for
negative)
←→
←→
←→
The unit conversion keys are [°F °C ], [ mmHg Kpa ], [ gal I ],
A result is displayed in decimal format if the integer, numerator,
denominator and fraction symbols are together more than 10 digits.
←→
←→
[ lb kg ] and [ oz g ]. The following example illustrates the general
procedure for converting values from one unit to another.
2. Functions that require pressing the function key before entering a
value, for example, [ DATA ] in statistics mode, and [ EXP ].
b
b
b
b
12345 [ a /c ] 5 [ a /c ] 16
5
12345 +5
16
= 12350.77
6
Overflow and Error Conditions
The symbol E appears when any of the following conditions occur.
Press [ ON/C ] to remove the overflow or error indicator.
DEG
DEG
12350.77
[ + ] 5 [ a /c ] 6 [ a /c ] 13
ENTER
3. Functions that require values to be entered before pressing the
13
→
←→
12 in = ? cm
98 cm = ? in
12 [ A B ] [ 2ndF ] [ in cm]
←
30.48
38.58
function key, for example, cos, sin, tan, cos –1, sin –1, tan –1, log, ln,
[
]
98 [ 2ndF ] [ A B ] [ 2ndF ]
←→
3
x 2, x –1
,
,
,
,
, and the unit
DEG
√
π
√
, x!, %, RND, ENG,
[ in cm ]
Converting Angular Units
When you attempt to perform a function calculation with a number
outside the allowable input range.
conversion functions.
•
You can specify an angular unit of degrees (DEG), radians (RAD), or
grads (GRAD). You can also convert a value expressed in one
angular unit to its corresponding value in another angular unit.
Statistics
4. Fractions.
When you attempt to divide a number by 0.
•
•
Press [ 2ndF ] [ STAT ] to enter statistics mode. The STAT indicator
appears on the display. In statistics mode you can calculate the
following single-variable statistics:
5. +/–
When you have pressed the [ ( ] key more than 15 times in a
single expression.
6. x y, X
√
The relation between the angular units is:
180° = radians = 200 grads
π
7. nPr, nCr
n
number of data items
sum of the values of all the data items
sum of the squares
When any result (whether intermediate or final) or the
•
•
To change the angular unit setting to another setting, press
[ DRG ] repeatedly until the angular unit you want is indicated in
the display.
•
•
Σx
Σx2
÷
accumulated total in memory is outside ±9.999999999 × 10 99
8. ×,
When there are more than six pending operations.
9. +, –
mean value
x
If the calculator becomes locked and pressing keys has no effect,
press [ M+ ] and [ ENG ] at the same time. This unlocks the calculator
and returns all settings to their default values.
→
After entering the value of an angle, press [ 2ndF ] [ DRG
repeatedly until the value is converted to the desired unit.
]
Corrections
x
2 − ( x)2/n
n −1
∑
∑
s
sample standard deviation
If you have made a mistake when entering a number and you have
not yet pressed an arithmetic operator key, just press [ CE ] to clear
the last entry. You can then input the desired number again.
Alternatively,you can delete digits one at a time by pressing the
DEG
90
90.
90° (deg)
= ? (rad)
= ? (grad)
2 − ( x)2/n
n
RAD
x
Basic Calculations
The following examples of basic calculations assume that your
calculator is in decimal base and with floating point display.
∑
∑
→
→
[ 2ndF ] [ DRG
[ 2ndF ] [ DRG
]
]
1.57
σ
population standard deviation
GRAD
100.00
→
backspace key: [ 00 0 ].
Continued on other side
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
DEG
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
STAT
données
[ DATA ] 5
[ DATA ] 5
[ DATA ] 5
[ DATA ] 5
[ DATA ] 9
[ DATA ] 9
[ DATA ] 9
5.
5.
√
[ cos –1
)=? rad
2 [
] [ 2ndF ] [ x –1] [ 2ndF ]
]
1
RAD
cos –1
(
0.79
2
tan –1 1 = ? grad
1 [ 2ndF ] [ tan –1
]
GRAD
5.
50.00
5.
Fonctions hyperboliques et hyperboliques inverses
9.
cosh1.5+sinh1.5
1.5 [ HYP ] [ cos ] [ + ] 1.5
ENTER
7 [ HYP ] [ 2ndF ] [ sin –1
1 [ HYP ] [ tan ]
DEG
4.48
9.
= ?
[ HYP ] [ sin ] [
]
sinh –1 7 = ?
]
DEG
DEG
9.
2.64
0.76
ENTER
[
[
]
0.00
6.13
8.00
2.59
49.00
347.00
2.42
12.
tanh 1 =
?
= ?
]
x
x
Coordonnées rectangulaires et polaires
Coordonnées rectangulaires Coordonnées polaires
n = ?
[ n ]
[ S ]
S = ?
Σx = ?
Σx 2 = ?
σ= ?
[ 2ndF] [ Σx ]
2
[ 2ndF ] [ Σx
[ 2ndF ] [ σ ]
]
σ
CP
[ 2ndF ] [ CP ] 12
USL
CP
LSL
CP
DEG
DEG
DEG
DEG
DEG
STAT
STAT
STAT
STAT
STAT
ENTER
CP = ?
[
[
] 2
2.
0.69
ENTER
]
CPK
USL
CPK
LSL
[ 2ndF ] [ CPK ]
12.00
2.00
a + b I = r (cosθ + i sinθ)
ENTER
]
CPK = ?
[
[
Remarque : Avant d'entreprendre un calcul de conversion de
coordonnées, vérifiez que vous avez spécifié l'unité
d'angle appropriée.
CPK
ENTER
]
0.57
Remarque : La calculatrice mémorise les données entrées jusqu'à la
sortie du mode Statistiques. Les données sont
conservées même en cas d'extinction automatique ou
manuelle de la calculatrice.
Conversion de coordonnées rectangulaires en polaires
DEG
Si a = 5 et b = 6,
combien valent r
→
5 [ a ] 6 [ b ] [ 2ndF ] [ R P ]
7.81
DEG
[ b ]
50.19
θ
et
?
Affichage des données de statistiques
ENTER
Appuyez sur [DATA ] ou [ ] en mode édition (ED) pour afficher
Conversion de coordonnées polaires en rectangulaires
les données statistiques entrées. (Si vous appuyez sur [ DATA ], le
numéro de données apparaît rapidement avant la valeur).
25 [ a ] 56 [ b ] [ 2ndF ]
→
[ P R ]
θ
Si r = 25 et
=
DEG
13.98
20.73
56°, combien
valent a et b ?
DEG
Ex.10 : Consultez les données entrées dans l'Ex. 9.
Méthode 1
[ b ]
Permutations et combinaisons
1. Appuyez sur [2ndF ] [ EDIT ] pour passer en mode édition.
n!
n!
nPr =
nCr =
2. Appuyez une fois sur [DATA ] pour afficher la première valeur de
données.
(n − r)!
r !(n − r)!
Combien de
DEG
DEG
DEG ED STAT
DEG ED STAT
ENTER
permutations de 4 7 [ 2ndF ] [ nPr ] 4 [
objets parmi 7 ?
]
840.00
35.00
→
1,5 secondes
dAtA
1
2.00
Combien de
3. Continuez d'appuyez sur [ DATA ] pour afficher chaque valeur de
données. Vous voyez successivement apparaître data 2, 5.00,
data 3, 5.00, data 4, 5.00, data 5, 5.00, data 6, 9.00, data 7, 9.00,
data 8, 9.00.
ENTER
combinaisons de 7 [ 2ndF ] [ nCr ] 4 [
4 objets parmi 7 ?
]
↔
Conversions de sexagésimal
Il est possible de convertir une valeur sexagésimale (degrés, minutes
et secondes) en valeur décimale en appuyant sur [ ] et de
convertir un nombre décimal en valeur sexagésimale en appuyant sur
[ 2ndF ] [ ].
décimal
Méthode 2
ENTER
4. Appuyez une fois sur [
données.
] pour afficher la première valeur de
DEG ED STAT
2.00
Les valeurs sexagésimales sont affichées comme suit :
ENTER
5. Continuez à appuyer sur [ ] pour afficher chaque valeur de
12 ꢀ 45
׀ 30 ׀ ׀ 5
= 12 degrés, 45 minutes, 30,5
secondes
données. Vous verrez apparaître successivement 5.00, 5.00,
5.00, 5.00, 9.00, 9.00, 9.00.
Remarque : Si le nombre total de chiffres d'une valeur DD, MM et
SS.SS dépasse 8, la valeur est tronquée.
Ajout d'une valeur de données
Ex. 11 : Pour ajouter une 9ème valeur de données égale à 10 au jeu de
Conversion de sexagésimal en décimal
données de l'Ex. 9.
12 deg., 45 min.,
30.5 sec.=?
12 [
[
] 45 [
] 30.5
]
DEG
DEG
12.76
DEG ED STAT
]
1. Appuyez sur [DATA ] 10
10.
Conversion de décimal en sexagésimal
2.12345 = ? 2.12345 [ 2ndF ] [
La calculatrice met à jour les statistiques dès l'entrée des données.
2 ꢀ 7
׀ 24 ׀׀ 42 Vous pouvez alors rappeler les statistiques pour obtenir :
= 6.56, n
x
= 9.00, S = 2.74, Σx = 59.00, Σx 2 = 447.00, σ= 2.59.
Calculs en base "n"
Conversion entre bases
Modification de données statistiques
Ex.12 : Modifiez la valeur de données 1 de l'Ex. 9 de 2 en 3.
Il est possible d'ajouter, soustraire, multiplier et diviser des nombres
binaires, octaux et hexadécimaux en plus des nombres décimaux.
Méthode 1
→
→
→
Sélectionnez la base voulue en appuyant sur [ BIN], [ OCT], [
1. Appuyez sur 2 [ 2ndF ] [ DEL ] 3
Méthode 2
→
HEX], ou [ DEC]. Les indicateurs BIN, OCT et HEX indiquent la
base utilisée (si aucun des indicateurs n'est affiché, vous utilisez la
base décimale).
DEG ED STAT
1. Appuyez sur [2ndF ] [ EDIT ]
0.00
2.00
Les touches actives dans une base sont :
Base binaire : [ 0 ] et [ 1 ]
DEG ED STAT
2. Appuyez sur 2 en appuyant sur [ DATA ]
ENTER
ou [
]
Base octale : [ 0 ] à [ 7 ]
DEG ED STAT
3. Entrez 3 pour effacer 2.
3.
Base décimale : [ 0 ] à [ 9 ]
ENTER
Base hexadécimale : [ 0 ] à [ 9 ] et [ A ] à [ F ]
4. Appuyez sur [ ] pour valider la modification.
DEG
→
[ 2ndF ] [ DEC] 31
→
5. Appuyez sur [2ndF ] [ EDIT ] pour quitter le mode Edition.
31.
11111.
37.
31 (base 10)
= ? (base 2)
= ? (base 8)
DEG BIN
DEG OCT
DEG HEX
[ 2ndF ] [ BIN]
Ex.13 : A partir de l'Ex.9, supprimez la première valeur de données
(égale à 2).
→
[ 2ndF ] [ OCT]
→
= ? (base 16)
[ 2ndF ] [ HEX]
→
Méthode 1
1F.
[ 2ndF ] [ HEX] 4 [ x ] 1B
DEG HEX
DEG
1. Appuyez sur 2 [ 2ndF ] [ DEL ] pour supprimer 2.
6C.
4 x 1B (base 16)
= ? (base 2)
[ ENTER ]
Méthode 2
BIN1101100.
108.00
→
[ 2ndF ] [ BIN]
→
DEG ED STAT
= ? (base 10)
= ? (base 8)
1. Appuyez sur [2ndF ] [ EDIT ]
0.00
DEG
[ 2ndF ] [ DEC]
→
DEG OCT
DEG ED STAT
[ 2ndF ] [ OCT]
154.
2. Appuyez sur 2 en appuyant sur [ DATA ]
2.00
5.00
ENTER
].
ou [
Nombres négatifs et compléments
Dans les bases binaire, octale et hexadécimale, les nombres négatifs
sont exprimés sous forme de compléments. Le complément est le
résultat de la soustraction du nombre de 10000000000 dans la base
considérée. Pour cela, appuyez sur [+/–] dans une base non
décimale.
DEG ED STAT
3. Appuyez sur [2ndF ] [ DEL ]
4. Appuyez sur [2ndF ] [ EDIT ] pour quitter le mode édition.
Erreur de suppression
Calculer le
complément du
nombre binaire
11011
Si vous tentez de supprimer une valeur qui n'existe pas dans le jeu de
données, dEL Error apparaît. (Les données existantes ne sont pas
modifiées.)
DEG BIN
→
[ 2ndF ] [ BIN ] 11011 [+/–]
1111100101.
Ex.14 : Supprimez 7 du jeu de données de l'Ex. 9.
DEG
STAT
Calculs sur les nombres complexes
1. Appuyez sur 7 [ 2ndF ] [ DEL ]
Appuyez sur [CPLX ] pour entrer en mode nombres complexes.
L'indicateur CPLX apparaît à l'écran. Vous pouvez ajouter, soustraire,
multiplier et diviser des nombres complexes.
dEL Error
DEG
STAT
2. Appuyez sur une touche pour effacer le
message.
0.00
Les nombres complexes sont généralement représentés sous la
forme a + b i, où a et b i sont les parties réelle et imaginaire.
Ex.15 : Supprimez 5 × 5 du jeu de données de l'Ex.9.
[ 2ndF ] [ CPLX ] 7 [ a ] 9 [+/–]
DEG CPLX
DEG
STAT
[ b ] [ + ] 15 [ a ] 10 [ b ]
ENTER
( 7 – 9 i ) +
(15 + 10 i) = ?
22.00
1.00
1. Appuyez sur 5 [ x ] 5 [ 2ndF ] [ DEL ]
[
]
dEL Error
DEG CPLX
[ b ]
DEG
STAT
2. Appuyez sur une touche pour effacer le
0.00
Remarque : Le calcul en mémoire est possible en mode complexe.
message.
Nombres pseudo-aléatoires
Appuyez sur [2ndF ] [ RND ] pour générer un nombre
pseudo-aléatoire compris entre 0.000 et 0.999.
Méthode d'entrée de données pondérées
Plutôt que d'entrer individuellement chacune des données, vous
pouvez entrer la valeur et le nombre d'occurrences de cette valeur
(jusqu'à 255). Les données de l'Ex.1 peuvent être entrées comme
suit :
Conversions d'unités
←→
←→
Les touches de conversion d'unité sont [°F °C ], [ mmHg Kpa ],
←→
←→
←→
[ gal I ], [ lb kg ], [ oz g ]. L'exemple ci-dessous illustre la
procédure générale de conversion de valeur d'une unité en une autre.
Valeur Nombre d'occurrences
Autre méthode
[ DATA ] 2
Attention : 1 gal UK – Cdn = 4.546092 litres et 1 gal US = 3.785412 litres.
DEG
2
5
9
1
4
3
→
←→
12 in = ? cm
12 [ A B ] [ 2ndF ] [ in cm]
←
30.48
38.58
[ DATA ] 5 [ x ] 4
[ DATA ] 9 [ x ] 3
98 [ 2ndF ] [ A B ] [ 2ndF ]
←→
DEG
98 cm = ? in
[ in cm ]
Où valeur 1 = 2, valeurs 2 à 5 = 5, et valeurs 6 à 8 = 9.
Statistiques
Conditions d'erreur
Appuyez sur [ 2ndF ] [STAT ] pour entrer en mode statistiques.
L'indicateur STAT apparaît à l'écran. En mode statistiques, vous
pouvez calculer les statistiques suivantes sur une variable :
L'indicateur FULL apparaît dans une des conditions ci-dessous.
L'entrée ultérieure de données n'est plus possible. Appuyez sur une
touche pour effacer l'indicateur. A condition de rester en mode
statistiques, les données entrées précédemment ne sont pas
modifiées.
n
nombre de valeurs de données
somme des valeurs de données
somme des carrés de valeurs
valeur moyenne
Σx
Σx2
Vous tentez d'entrer plus de 80 valeurs de données.
•
•
Le nombre d'occurrences d'une valeur de données est supérieur
à 255
x
x2 − ( x)2 /n
n − 1
∑
∑
s
écart type d'échantillon
écart type de population
Le produit du nombre de valeurs de données et du nombre
d'occurrences est supérieur à 20400.
•
x2 − ( x)2 /n
∑
∑
σ
n
USL−LSL
6 σ
CP
capacité de précision
CPK
capacité de traitement Min(CPU, CPL)
USL− x
3 σ
x −LSL
3 σ
où CPU =
CPL =
Remarque : En mode statistiques, toutes les touches de fonction
sont disponibles sauf celles utilisées pour les calculs en
base "n".
© Copyright 2002 Hewlett-Packard Development Company, L.P.
Toute reproduction, adaptation ou traduction sans accord préalable
écrit est strictement interdite, sous couverture des lois sur la
protection de la propriété intellectuelle.
Ex. 9 : Entrez les données suivantes {2, 5, 5, 5, 5, 9, 9, et 9} et
calculez Σx, Σx2, n, , S, CP, et CPK, où valeur USL =
x
12 et valeur LSL = 2.
Imprimé en Chine.
HDPMR178127 MWB
DEG
DEG
STAT
STAT
En mode STAT
Entrez toutes les
[ 2ndF ] [ STAT ]
[ DATA ] 2
0.00
2.
Référence HP : F2212-90002
|