Sharp EL-9650 User manual

Graphing Calculator
EL-9650/9600c/9450/9400
Handbook Vol. 2
Programmes
EL-9650 EL-9450

1. Heron's Formula 1
2. Calculating Tension 2
3. Involute (Inverse Involute) 4
4. Calculating Illuminance and Luminous Intensity 6
5. Calculating Simple Harmonic Oscillation 8
6. Electric Power Consumed on an AC Circuit 10
7. Angle of Vector* 12
8. Linear Transformation* 14
9. Moving Average 16
10. Creating a Graph of Experimental Data 18
11. Ordinary Differential Equations 20
12. Analysing with One-way Layout Method 22
13. Calculating Parabolic Motion 25
*only for EL-9650/9600c
Contents
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1. Entering and Editing a Programme:
Programmes can be entered and edited either by pressing the calculator keys or by downloading from a PC.
To download programmes from a PC, you will need the CE-LK1P PC link software (sold separately).
A. Using calculator keys
●
Creating a new programme:
1. Press to display the programme menu.
2. Press to select the new programme menu. (See right)
3. Enter the programme title, then press .
4. Enter the programme.
5. Press to finish programming.
●
Editing a programme:
1. Press to display the programme menu.
2. Press and choose the number of the programme you wish to edit.
3. Press to finish editing.
B. Downloading from PC
●
Creating a new programme:
1. Using the CE-LK1P, select the Model Type from the Tools menu
and click on the same model as your calculator.
2. Select New from the File menu.
3. Enter a programme name in Title:.
4. Enter a programme. (For details on entering a programme, refer to
the operation manual.)
●
Programmes can also be downloaded from Sharp’s website at
http://sharp-world.com/products/calculator/education/program/index.html
instead of creating a new programme.
Read this first
This handbook was produced for practical application of the SHARP EL-9650/9600c and EL-9450/9400
Graphing Calculator. Both calculators include a highly convenient programming function, which enables
automatic processing of both simple and complex calculations any number of times.
Note: Certain problems can not be solved with the EL-9450/9400 as indicated in contents.
(See right)
ENTER
ENTER
PRGM
2nd F
2nd F QUIT
PRGM
2nd F
2nd F QUIT
C
B
(See right)

2. Executing a programme:
1. Press to display the execute menu.
2. Press and choose the number of the programme you wish to
execute.
3. Follow the instructions.
●
Sending programmes from a PC:
1. Using the CE-LK1P, select the Communication Port from
the Link menu and click on the port to be used.
2. Turn off the EL-9650/9600c/9450/9400 and connect it to the PC.
3. Turn on the EL-9650/9600c/9450/9400
4. Select Send… from the Link menu of the CE-LK1P (See right)
5. Specify the kind of drive, folder, and file, then select the file
to be sent from the file list, and click on the Select button.
6. Click on the OK button.
Note : For further details refer to the manual.
ENTER
PRGM
2nd F
3. Deleting a programme:
Press and then choose to select the programme to
be deleted.
Note: Do not try to erase a programme by resetting all memories to the initial condition as
programme data to be stored will also be deleted. Also, it is advised to use the CE-
LK1P PC link software to back up any programmes not to be erased.
C5
OPTION
2nd F
4. Using the keys:
Press to use secondary functions (in yellow).
To select “sin
-1
”: ➔Displayed as follows:
Press to use the alphabet keys (in blue).
To select A: ➔Displayed as follows:
Press to continue input of blue letters.
To input ABC: or
(To return to the normal function, press again.)
2nd F
A
2nd F 2nd Fsin sin
-1
ALPHA
ALPHA
sin
ALPHA
2nd F
A-LOCK
ALPHA ALPHA ALPHA
ALPHA
ABCA BC
2nd F
A-LOCK
sin
-1
A
(See right)
A

5. Troubleshooting:
Following is a list of error codes and error messages.
When errors occur, refer to pages 12, 254, or 27 of the manual.
01 Syntax Syntax error in equation or programme
02 Calculate Execution of a division using 0, calculation beyond calculation range, etc.
03 Nesting Reservation of 14 or more numerical values or 32 or more functions during execution.
04 Invalid Matrix definition error
05 Dimension Inconsistency in the dimension of matrix during arithmetic of a matrix or dimension of list for
STAT calculation.
07 Invalid DIM Size of list and matrix input for calculation exceeds calculation range.
08 Argument Inconsistency in argument of the structured function
09 Data Type Invalid data type used in calculation
11 No define Undefined list or matrix
12 Domain Argument definition outside of domain
13 Increment Increment error
17 Stat Med Med-Med law (statistic) error
20 No Argument No argument entered
21 Not pair ∫dx Equation definition (∫and dx as a pair) for integral calculus does not follow syntax.
22 Not pair [ ] Not paired with specified “[ ]”
23 Not pair ( ) Not paired with specified “( )”
24 Not pair { } Not paired with specified “{ }”
32 No data Data does not exist
33 Graph Type Error in graph type setting
37 No title No title entered
38 Too many obj More than 30 objects selected
40 Lbl duplicate Same label name is used more than once within a programme
41 Lbl undefined Label is not defined for Goto or Gosub
42 Lbl over More than 50 labels are used within a programme
43 Gosub stack Nesting of more than 10 subroutine stacks
44 Line too long One line of programme exceeds more than 160 characters
45 Can’t return Use of return command without jumping from subroutine
46 Strage full Attempt to create a file exceeding 99 (delete unnecessary files)
47 Coord type Invalid coordinate system for command
90 Memory over Over memory capacity
99 System error User memory space cannot be secured
Error content
Error
code
Error message

EL-9650/9600c Graphing Calculator
3
DisplayStep Key Operation
1
2
Specify the program mode.
Select the title INVOLUTE.
(Display of angle of obliquity)
Exercise
(1) Find the angle of obliquity when the involute value is 0.0050912 and the initial
value is 10.
(2) Find the involute value when the angle of obliquity is 14.1.
Set up condition: angle unit in Deg Mode and decimal point in
Float Pt Mode.
****
4
(Display of involute value)
5
*
Select involute calculation.
Select inverse involute
calculation.
Enter the initial value and the
involute value.
Enter the value of the angel
of obliquity.
5
CL
1B
SET UP 2nd F
1C
2nd F PRGM A
ENTER
0005091•
ENTER 1
ENTER 01
ENTER 2
ENTER
ENTER
14 1•
EL-9650/9600c Graphing Calculator
Involute (Inverse Involute)
Use the involute function for calculating gears etc. to find the angle of obliquity from
the initial value and involute value.
Conversely, calculate the involute value from the angle of obliquity.
Calculation
Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:
FLOWCHART
PARAMETERS
PROGRAM LIST
(REAL MODE)
Selection of type
Entry of initial
value and
involute value
Calculation of
angle of obliquity
Display of angle of obliquity
Start
End
start
Y
ANGLE
INVO
CALPRESS
Y
Y
N
N
N
Calculation of involute
value (display)
Entry of angle
of obliquity
Enter 1 or 2.
To calculation of involute.
Calculation of involute.
Enter initial value and
involute value.
Angle of obliquity
calculated.
Judgment on repetition
of calculation of angle
of obliquity.
Calculation of inverse
involute. Enter angle
of obliquity.
Involute value calculated.
Involute value displayed.
To inverse involute calculation
Returns to START if entry
neither 1 nor 2.
θ i +1 = θ i -= q i -
f(θ
i )
f'(θ)tan
2
θ i
tanθ i - θ i -a
f ( θ ) = a - inv q SP : involute curve
S : involute starting point
θ: angle of obliquity of point P
Name of parameter
D, R, T, J
S
Z
Content
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity
Name of parameter
θ
I
A
B
Content
angle of obliquity
involute value
input and output of angle
input of initial value
S = 2
int(10
8
D) 0
S = 1
0
q
Rg
P
Sa
θ
θ
Label START
ClrT
Print "SELECT 1/2
Input S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
Input B
B Z
Print "Input INVO
Input I
I J
Label CALPRESS
tan Z T
πZ/180.0 R
(T-R-J)/T
2
D
180.0 (R-D)/πZ
If int (
10 8 D)≠0 Goto CALPRESS
Z A
Print "ANGLE
Print A
End
Label INVO
Print "Input ANGLE
Input A
A θ
tanθ -πθ/180 I
Print "INVOLUTE
Print I
End
Title : INVOLUTE
4
6. Page Layout
Note: This handbook is only an example of how to use programming function of the EL-9650/9600c.The layout may vary with each screen.
2
Introduction
Brief explanation and
purpose of the section
Exercise
Example of problem to be
solved in the section
Set Up Condition
Important set up condition
before starting the exercise
in order to obtain correct
answers
Step
A step-by-step guide to solving the problems
and an explanation of the display
Key Operation
Illustration of the keys to be
operated
Display
Illustration of the calculator
screen as it should appear
if each step is carried out
correctly
Calculation
The formula to be used
in calculation and
definition of terms
Flowchart
Summary of steps from
start to end
Programme List
Procedure of data to
be entered
Parameters
Definition of the
parameters used in the
programme
When the mark
✽
appears on the key:
●
Same series of key strokes can be done
with screen touch.
●
Key operations may also be carried out
with the cursor (not shown).
(When using EL-9650/9600c)

EL-9650/9600c/9450/9400 Graphing Calculator
Heron's Formula
Use Heron's formula to find the area of a triangle when the sides (A,B,C) of the
triangle are known.
Calculation
S = D (D - A) (D - B) (D - C)
D = (A + B + C)
2
AC
B
FLOWCHART
PARAMETERS
PROGRAMME LIST(REAL MODE)
Calculation of area
Display of area
Calculation of D
Entry of sides
Start
End
Enter sides A, B and C.
Value of D calculated.
Area of triangle
displayed.
Area S calculated.
Title : HERON
Print "Input LENGTH
Input A
Input B
Input C
(A+B+C)/2 D
(D (D-A) (D-B) (D-C) ) S
Print "S =
Print S
End
Name of parameter
A
B
C
Content
value of side A
value of side B
value of side C
Name of parameter
D
S
Content
value of D
area
Exercise
Find the area of a triangle when sidesA,B and C are 20,35 and 40cm respectively.
Key OperationStep Display
1
2
Specify the programme
mode.
Select the title HERON.
*
The area is approximately
350cm2.
3
(Display of area)
Enter the values A, B and C.
1
2nd F PRGM
2 ENTER
A
ENTER ENTER
035
40
(When using EL-9650/9600c)
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EL-9650/9600c/9450/9400 Graphing Calculator
Calculating Tension
Use the law of sines to find the tension when a pole of weight W is suspended with
two strings, and the strings are balanced with the angles from the vertical line A and B.
Calculation
FLOWCHART
PARAMETERS
PROGRAMME LIST (REAL MODE)
Calculation of tensions
Display of tensions
Calculation of denominator
Entry
Start
Enter angles and weight
A, B and W.
Denominator in law of sines
calculated. C= sin (A + B)
Tensions T and S displayed.
Tensions T and S calculated.
T = W sin B/C
T = W sin A/C
Name of parameter
A
B
C
Content
angle A
angle B
sin(A+B)
Name of parameter
S
T
W
Content
tension S
tension T
weight
T
sin B =S sin A =W sin (A+B)
sin B
sin (A+B)
T = W
sin A
sin (A+B)
S = W
T, S : tension W : weight
A, B : angles (6 sexagesimal numbers)
A
B
S
W
T
A
vertical line
T
GS
W
B
Print "Input ANGLE
Input A
Input B
Print "Input WEIGHT
Input W
sin (A+B) C
W sin B/C T
W sin A/C S
Print "TENSION
Print "T=
Print T
Print "S=
Print S
End
Title : TENSION
2
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EL-9650/9600c/9450/9400 Graphing Calculator
*
3
DisplayStep Key Operation
1
2
Specify the programme mode.
Select the title TENSION.
Tension T is 21.840kg and
S is 23.795kg.
Exercise
Calculate the tension assuming weight=40kg, angle A=30˚ 15' 20", and angle
B=27˚ 45' 40". Enter the angles with sexagesimal numbers.
Set up condition: decimal point digit number in TAB 3 Mode, decimal
point in Fix Mode, and angle unit in Deg Mode.
******
4
Enter the values of angles
A and B.
Enter the value of weight.
3
CL2C SET UP 2nd F 3D1B
3
2nd F PRGM A
ENTER
ENTER
ENTER
0 1520
27 4540
40
•
•
(When using EL-9650/9600c)
motomotomotomoto
moto
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EL-9650/9600c/9450/9400 Graphing Calculator
Involute(Inverse Involute)
Use the involute function for calculating gears etc. to find the angle of obliquity
from the initial value and involute value.
Conversely, calculate the involute value from the angle of obliquity.
Calculation
Involute function : inv θ = tan θ - θ[rad]
Use Newton's method to find the inverse involute:
FLOWCHART
PARAMETERS
PROGRAMME LIST (REAL MODE)
Selection of type
Entry of initial
value and
involute value
Calculation of
angle of obliquity
Display of angle of obliquity
Start
End
start
Y
ANGLE
INVO
CALPRESS
Y
Y
N
N
N
Calculation of involute
value (display)
Entry of angle
of obliquity
Enter 1 or 2.
To calculation of involute.
Calculation of involute.
Enter initial value and
involute value.
Angle of obliquity
calculated.
Judgment on repetition
of calculation of angle
of obliquity.
Calculation of inverse
involute. Enter angle
of obliquity.
Involute value calculated.
Involute value displayed.
To inverse involute calculation
Returns to START if entry
neither 1 nor 2.
θ i +1 = θ i -= θ i -
f(θ i )
f'(θ)tan
2
θ i
tanθ i - θ i -a
f (θ) = a - invθSP: involute curve
S : involute starting point
θ: angle of obliquity of point P
Name of parameter
D, R, T, J
S
Z
Content
working variable for calculating
selecting calculation type
(S=1: involute calculation)
(S=2: inverse involute calculation)
initial value, angle of obliquity
Name of parameter
θ
I
A
B
Content
angle of obliquity
involute value
input and output of angle
input of initial value
S = 2
int(10
8
D) 0
S = 1
0
q
Rg
P
Sa
θ
θ
Label START
ClrT
Print "SELECT 1/2
Input S
If S=1 Goto ANGLE
If S=2 Goto INVO
Goto START
Label ANGLE
Print "Input BEGIN
Input B
B Z
Print "Input INVO
Input I
I J
Label CALPRESS
tan Z T
πZ/180.0 R
(T-R-J)/T
2
D
180.0 (R-D)/πZ
If int ( 10 8 D)≠0 Goto CALPRESS
Z A
Print "ANGLE
Print A
End
Label INVO
Print "Input ANGLE
Input A
A θ
tanθ -πθ/180 I
Print "INVOLUTE
Print I
End
Title : INVOLUTE
4
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EL-9650/9600c/9450/9400 Graphing Calculator
3
DisplayStep Key Operation
1
2
Specify the programme mode.
Select the title INVOLUTE.
(Display of angle of obliquity)
Exercise
(1) Find the angle of obliquity when the involute value is 0.0050912 and the initial
value is 10.
(2) Find the involute value when the angle of obliquity is 14.1.
Set up condition: angle unit in Deg Mode and decimal point in
Float Pt Mode.
****
4
(Display of involute value)
5
*
Select involute calculation.
Select inverse involute
calculation.
○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○
Enter the initial value and the
involute value.
Enter the value of the angle
of obliquity.
5
CL
1B
SET UP 2nd F
1C
2nd F PRGM A
ENTER
0005091•2
ENTER 1
ENTER 01
ENTER 2
ENTER
ENTER
14 1•
(When using EL-9650/9600c)
motomoto
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EL-9650/9600c/9450/9400 Graphing Calculator
Calculating Illuminance and Luminous Intensity
Enter the luminous intensity of the luminous source, the distance, and the angle between
the perpendicular line and light ray, to find the illuminance of the illuminated side.
Conversely, find the luminous intensity of the source from the illuminance of the
illuminated side.
Calculation
FLOWCHART
PARAMETERS
PROGRAMME LIST(REAL MODE)
Selection of type
To subroutine To subroutine
Start
End
Return
Subroutine
start
CANDELA LUX
DISTANCE
Y
N
Entry of
luminous intensity
Calculation of
luminous intensity
Entry of
illuminance
Calculation of
illuminance
Display of
illuminance
Display of
luminous intensity
Entry of distance and angle
Enter 1 or 2.
To calculation of
luminous intensity.
To calculation of
illuminance.
Jumps to subroutine
DISTANCE.
Enter illuminance or
luminous intensity.
Illuminance or luminous
intensity calculated.
Illuminance or luminous
intensity displayed.
Subroutine for entry of
distance and angle.
Returns to calling program.
Entry.
l : luminous intensity [candela] i : illuminance [lux]
r: distance [m] θ: angle [˚ ]
Name of parameter
I
K
R
S
Content
illuminance of illuminated side
luminous intensity of luminous source
distance
selecting calculation type
(S=1:
calculation of luminous intensity )
(S=2: calculation of illuminance)
Name of parameter
θ
A
L
D
C
Content
angle
input of angle
input and calculating luminous intensity
input of distance
input and calculating illuminance
Label START
ClrT
Print "CANDELA=1 LUX=2
Print "SELECT 1/2
Input S
If S=1 Goto CANDELA
If S=2 Goto LUX
Goto START
Label CANDELA
Gosub DISTANCE
Print "Input LUX
Input L
L I
R
2
I/cos θC
Print "CANDELA
Print C
End
Label LUX
Gosub DISTANCE
Print "Input CANDELA
Input C
C K
K cos θ/R
2
L
Print "LUX
Print L
End
Label DISTANCE
Print "Input DISTANCE
Input D
D R
Print "Input ANGLE
Input A
A θ
Return
S = 2
S = 1
i = r
2
l cos θl = cos θ
r
2i
r
A
A
Illuminance i
Luminous Intensity l
θ
Title : CAND LUX
6
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EL-9650/9600c/9450/9400 Graphing Calculator
3
DisplayStep Key Operation
1
2
Specify the programme mode.
Select the title CAND LUX.
(Display of luminous intensity)
Exercise
(1) Find the luminous intensity of the luminous source of distance 10m, angle 60˚
and illuminance 20 lux.
(2) Find the illuminance of the illuminated side of distance 10m, angle 60˚ and
luminous intensity 4000 candela.
Set up condition: angle unit in Deg Mode and decimal point in
Float Pt Mode.
****
4
(Display of illuminance)
*
Select calculation of luminous
intensity.
Select calculation of illuminance.
Enter the values of distance,
angle, and luminous intensity.
Enter the values of distance,
angle, and illuminance.
7
CL
1B
SET UP 2nd F
1C
2nd F PRGM A
ENTER 1
ENTER
10
20
60 ENTER ENTER
ENTER ENTER
ENTER
ENTER
ENTER
10
60
4000
2
(When using EL-9650/9600c)
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EL-9650/9600c/9450/9400 Graphing Calculator
Calculating Simple Harmonic Oscillation
Enter period, amplitude and time to calculate displacement at specified time,
acceleration, angular velocity, and velocity. Also, display the changes during the
entered time period on a graph.
Calculation
FLOWCHART PROGRAMME LIST (REAL MODE)
Entry of period
and amplitude
Entry of time
Start
CALC
Calculation of
angular velocity, etc.
A : amplitude
t : time [sec]
T : period [sec]
ω : angular velocity [rad/sec]
angular velocity : ω =
acceleration : a = -ω2x velocity : v = A ω cos (ω t)
Tdisplacement : x = A sin (ω t)
Ax
0ωtv
0 v
ax
2πA
2π
+
+
++
ωt
Display of
calculation result.
Graph display
Display clear
Calculation of
range and scale
Print "Input PERIOD
Input P
P F
Print "Input AMPLITUDE
Input A
A D
Label CALC
Print "Input TIME
Input T
T E
2 π/F W
D sin (W E) H
-(W
2
) H B
D W cos (W E) V
Print "ANGULAR VELOCITY
Print W
Print "MAGNITUDE
Print H
Print "ACCELERATION
Print B
Print "VELOCITY
Print V
Wait
E/10 X scl
D/5 Y scl
0 Xmin:E Xmax
-D Ymin:D Ymax
Draw D sin (W X)
Wait
ClrT
ClrG
Goto CALC
Angular velocity, displacement,
acceleration and velocity
calculated.
W = angular velocity
H = displacement
B = acceleration,
V = velocity
Calculation result of angular
velocity, displacement,
acceleration and velocity
displayed.
Text and graph display cleared.
Range set and graph displayed.
Function: Y = D sin (W X)
X is time increase.
Xmin ... 0, Xmax ... E, Xscl ... E/10
Ymin ... -D, Ymax ... D, Yscl ... D/5
Title : OSCILLAT
8
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EL-9650/9600c/9450/9400 Graphing Calculator
3
DisplayStep Key Operation
1
2
Specify the programme mode.
Select the title OSCILLAT.
(Display of angular velocity)
(Display of displacement)
(Display of acceleration)
(Display of velocity)
Exercise
Calculate angular velocity, etc., using period ππ
ππ
π, amplitude 1 and time 3 seconds and
display the changes on a graph.
Set up condition: angle unit in Rad Mode and decimal point in
Float Pt Mode.
****
4(Display of graph of simple
harmonic oscillation)
5
*
PARAMETERS
Name of parameter
B
E
V
W
H
Xscl
Yscl
Content
acceleration
time
velocity
angle of velocity (ω)
displacement
x-axis scale
y-axis scale
Name of parameter
A
P
T
D
F
X
Content
input of amplitude
input of period
input of time
amplitude
period
time increase
Enter the values of period,
amplitude, and time.
9
CL
2B
SET UP 2nd F
1C
2nd F PRGM A
2nd F 1 ENTER
π
ENTER
ENTER
ENTER
ENTER
3
(When using EL-9650/9600c)
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EL-9650/9600c/9450/9400 Graphing Calculator
Electric Power Consumed on an AC Circuit
Enter the voltage effective value, frequency and resistance value to find the power
value of the circuit with resistance R. Draw a graph of the changes in power over a
period of time.
Calculation
FLOWCHART
PARAMETERS
PROGRAMME LIST (REAL MODE)
Data entry
Calculation of power
Calculation of range
Display of power
Display of graph
Start
End
Enter data (resistance, voltage and
frequency).
Power calculated.
W = angular velocity
M = maximum voltage
N = maximum current
I = effective value of current
Z = power
Range for graph calculated.
Xmax, Xscl, Ymax, Yscl
Power displayed. (value of Z)
Function: Y = N M (sin (W X))
2
Print "Input RESISTANCE
Input R
Print "Input VOLTAGE
Input V
Print "Input FREQUENCY
Input F
R T
V D
F S
2 πS W
D √2 M
M/T N
N/√2 I
D I Z
1/S Xmax
Xmax/10 Xscl
N M Ymax
Ymax/10 Yscl
Print "WATT=
Print Z
Wait
0 Xmin
0 Ymin
Draw N M (sin (W X))2
End
P : power consumption I : effective value of current
V : effective value of voltage
Name of parameter
S
I
T
D
W
N
M
Xmax
Content
frequency
effective value of current
resistance value
effective value of voltage
angular velocity
maximum value of current
maximum value of voltage
maximum value of x-axis
Name of parameter
Xscl
Ymax
Yscl
V
R
F
Z
Content
scale of x-axis
maximum value of y-axis
scale of y-axis
input of voltage
input of resistance value
input of frequency
value of power
I0= N •
sin ω•t V0= M •sin ω•t P0= l0•V0
P0: change in amount of power with time
I0: change in amount of current with time
V0: change in amount of voltage with time
N: maximum value of current M: maximum value of voltage
ω: angular velocity (2 πS) t : time S : frequency
RI
V
Title : AC POWER
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EL-9650/9600c/9450/9400 Graphing Calculator
3
DisplayStep Key Operation
1
2
Specify the programme mode.
Select the title AC POWER.
(Display of graph)
Exercise
Find the power value of an AC circuit with resistance value 150Ω, voltage effective
value 100V and frequency 50Hz and display on a graph the changes in power over
a period of time.
Set up condition: angle unit in Rad Mode and decimal point in
Float Pt Mode.
****
(Display of value power)
*
Enter the resistance value,
voltage effective value, and
frequency.
11
CL2B
SET UP 2nd F
1C
2nd F PRGM A
0 ENTER 15
0 ENTER 10
0 ENTER 5
ENTER
(When using EL-9650/9600c)
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EL-9650/9600c Graphing Calculator
A
ngle of Vector
Use the matrix operation feature to find the angle θwhich forms the standard vector
and vector. The angle can be calculated at one time against the multiple vectors.
Calculation
FLOWCHART PROGRAMME LIST(MATRIX MODE)
Entry of number
of vectors
Definition of arrays
Start
End
K = K + 1
Calculation of
component of
standard vector
Calculation of
inner product
Entry of standard
vector data
Enter no. of vectors for which
angles are calculated.
Arrays defined.
Counter for data entry.
Enter x component and Y component
of standard vector.
Product of matrices A and B
calculated.
Length component of standard
vector (scalar) calculated.
Calculating vector inner product a•b = | a | | b | cos θ
Use the above expression to derive the following expression
←
←←
←←
←←←
θ= cos-1 a•b
matA, matB, matC.
DATA
Vector data entry
Enter x component and Y
component of each vector.
K < M
Entry repeated by no. of vectors.
Y
N
Angle calculated and displayed.
CALC I = I + 1
Counter for calculation of angle.
I > M
Y
N
Calculation repeated by no.
of vectors.
END
Length component of vector
(scalar) calculated.
Calculation of
component of vector
Calculation of angle
and display of angle
0 I
0 K
Print " Input NUMBER
Input N
N M
{M,2} dim (mat A)
{2,1} dim (mat B)
{M,1} dim (mat C)
Label DATA
K + 1 K
Print " Input VECTOR
Print K
Input X
X mat A(K,1)
Input Y
Y mat A(K,2)
If K<M Goto DATA
Print "Input FUNDAMENTAL VECTOR
Input X
X mat B(1,1)
Input Y
Y mat B(2,1)
√(mat B(1,1)2+mat B(2,1)2) B
mat A mat B mat C
Label CALC
Ι+ 1 Ι
If I>M Goto END
√ (mat A(I,1)2+mat A(I,2)2) A
cos-1 (mat C(I,1)/ (A B)) θ
Print "ANGLE OF VECTOR
Print I
Print "θ=
Print θ
Wait
Goto CALC
Label END
End
| a | | b |
Title : VECTOR
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EL-9650/9600c Graphing Calculator
3
DisplayStep Key Operation
1
2
Specify the programme mode.
Select the title VECTOR.
Exercise
Calculate the angle formed by the following 3 vectors and standard vector (2,3).
vector 1 (5, 8)
vector 2 (7, 4)
vector 3 (9, 2)
Set up condition: angle unit in Deg mode, and decimal point in Float Pt
mode.
****
4
5
(Display of angle of vector 1)
6(Display of angle of vector 2)
(Display of angle of vector 3)
PARAMETERS
Name of parameter
A
B
I
K
M
X
Y
Content
vector scalar quantity
standard vector scalar quantity
calculating counter
input counter
number of vectors
input of x component
input of y component
Name of parameter
θ
K
N
mat A
mat B
mat C
Content
vector angle
display
input of number of vectors
vector components
standard vector components
vector inner product
*
Enter the number of vectors.
Enter the values of vector 1.
Enter the values of vectors
2 and 3.
Enter the value of standard
vector.
13
CL
1B
SET UP 2nd F
1C
2nd F PRGM A
3 ENTER
5 ENTER 8 ENTER
7 ENTER 4 ENTER
9 ENTER 2 ENTER
2 ENTER 3 ENTER
ENTER
ENTER
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EL-9650/9600c Graphing Calculator
Linear Transformation
Use the matrix to find four types of the linear transformation of x-axis symmetric
transformation, y-axis symmetric transformation, similar transformation and
revolution around the origin.
Calculation
FLOWCHART PROGRAMME LIST
(MATRIX MODE)
Array declaration
Entry of coordinates (X,Y)
Start
End
Entry of type
To label XSYMMETRY
Declare array size, etc.
matH(2,2), matD(2,1), matA(2,1)
Enter coordinates before transformation.
Type of transformation specified
with no from 1 to 4.
Jumps to destination corresponding
to entered number.
XSYMMETRY
Data set of x-axis symmetric transformation
matH(1,1) = 1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = -1
YSYMMETRY
Data set of y-axis symmetric transformation
matH(1,1) = -1, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = 1
{2, 2} dim(mat H)
{2, 1} dim(mat D)
{2, 1} dim(mat A)
Print "Input POINT
Input X
Input Y
X mat D(1, 1)
Y mat D(2, 1)
Label TYPE
Print "SELECT 1/2/3/4
Input S
ClrT
If S=1 Goto XSYMMETRY
If S=2 Goto YSYMMETRY
If S=3 Goto SIMRATIO
If S=4 Goto ROTATE
GotoTYPE
Label XSYMMETRY
1 mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
-1 mat H(2, 2)
Goto TRANS
Label YSYMMETRY
-1 mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
1 mat H(2, 2)
Goto TRANS
Label SIMRATIO
Print "Input
SIMILITUDE RATIO
Input R
R K
K mat H(1, 1)
0 mat H(2, 1)
0 mat H(1, 2)
θmat H(2, 2)
Goto TRANS
Label ROTATE
Print "Input ANGLE
Input A
A B
cos B mat H(1, 1)
sin B mat H(2, 1)
-sin B mat H(1, 2)
cos B mat H(2, 2)
Label TRANS
mat H mat D mat A
Print "mat A(1, 1)
Print mat A(1, 1)
Print "mat A(2, 1)
Print mat A(2, 1)
End
=
X'
Y'
() ()
X
Y
1 0
0 -1
() ()
(())()
()()
() ()()
1. Symmetric transformation to
x-axis (Case 1)
=
X'
Y' X Y
-1 0
01
2. Symmetric transformation to
y-axis (Case 2)
=
X'
Y' X Y
K0
0 K
3. Similar transformation with ratio of
similitude K around origin (Case 3)
=
X'
Y' X Y
cos B -sin B
sin B cos B
4. Transformation revolving around
only angle B at the origin (Case 4)
s = 1
To label YSYMMETRY
s = 2
Y
Y
N
To label SYMRATIO
s = 3 Y
N
To label ROTATE
Label XSYMMETRY Label YSYMMETRY
Transformation data set Transformation data set
Label SIMRATIO Label ROTATE
Entry of ratio of similitude
Entry of angle
Data set of transformation
Coordinate transformation
Display of coordinates after transformation
Data set of transformation
s = 4 Y
N
N
TYPE
Data set of transformation by revolving
Entry of angle (A)
matH(1,1) = cos B, matH(2,1) = sin B,
matH(1,2) = -sin B, matH(2,2) = cos B,
Matrix H multiplied by matrix D.
Coordinates displayed.
SIMRATIO
Data set of similar transformation
Entry of ratio of similitude (R)
matH(1,1) = K, matH(1,2) = 0,
matH(2,1) = 0, matH(2,2) = θ
Title : LINE TRNS
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