Casio fx-9750GIII: Sequence of Rotated Points
Introduction
The program ROTSEQ generates a 2 row matrix from the sequence:
[ [ x_n+1 ] [ y_n+1 ] ] = A * [ [ cos θ, -sin θ ] [ sin θ, cos θ ] ] * [ [ x_n ] [ y_n ] ]
The required inputs are:
You will set the angle mode to Degree, Radian, or Gradian
A = multiplier
θ = angle
x1 = initial x point
y1 = initial y point
N = number of steps
Casio fx-9750GIII Program ROTSEQ
This can be used on most if not every modern Casio Graphing calculator.
"EWS 2020-06-07"
Menu "ANGLE","DEGREE",1,"RADIAN",2,"GRADIAN",3
Lbl 1:Deg:Goto 4
Lbl 2:Rad:Goto 4
Lbl 3:Gra:Goto 4
Lbl 4
"F=A*MAT*[[X][Y]]"
"A"?->A
"θ"?->θ
"X1"?->X
"Y1"?->Y
"STEPS"?->N
[[X][Y]]->Mat A
Mat A->Mat B
For 1->I To N
[[cos θ,-sin θ][sin θ,cos θ]]*Mat A->Mat A
Augment(Mat B,Mat A)->Mat B
Next
"FINAL RESULTS:"◢
Mat B
Example
A = 0.5
θ = 10 grads (Gradian mode)
x1 = 1
y1 = -1
N = 5 (5 steps)
I don't think I ever used gradian angle units on this blog before, so why not?
Results are shown and rounded to 2 decimal places
Mat B:
[ 1.00 1.14 1.26 1.34 1.40 1.41 ]
[ -1.00 -0.83 -0.64 -0.44 -0.22 0.00 ]
The next blog post will be on July 5 since tomorrow will be the 4th of July (Happy Birthday, United States).
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Introduction
The program ROTSEQ generates a 2 row matrix from the sequence:
[ [ x_n+1 ] [ y_n+1 ] ] = A * [ [ cos θ, -sin θ ] [ sin θ, cos θ ] ] * [ [ x_n ] [ y_n ] ]
The required inputs are:
You will set the angle mode to Degree, Radian, or Gradian
A = multiplier
θ = angle
x1 = initial x point
y1 = initial y point
N = number of steps
Casio fx-9750GIII Program ROTSEQ
This can be used on most if not every modern Casio Graphing calculator.
"EWS 2020-06-07"
Menu "ANGLE","DEGREE",1,"RADIAN",2,"GRADIAN",3
Lbl 1:Deg:Goto 4
Lbl 2:Rad:Goto 4
Lbl 3:Gra:Goto 4
Lbl 4
"F=A*MAT*[[X][Y]]"
"A"?->A
"θ"?->θ
"X1"?->X
"Y1"?->Y
"STEPS"?->N
[[X][Y]]->Mat A
Mat A->Mat B
For 1->I To N
[[cos θ,-sin θ][sin θ,cos θ]]*Mat A->Mat A
Augment(Mat B,Mat A)->Mat B
Next
"FINAL RESULTS:"◢
Mat B
Example
A = 0.5
θ = 10 grads (Gradian mode)
x1 = 1
y1 = -1
N = 5 (5 steps)
I don't think I ever used gradian angle units on this blog before, so why not?
Results are shown and rounded to 2 decimal places
Mat B:
[ 1.00 1.14 1.26 1.34 1.40 1.41 ]
[ -1.00 -0.83 -0.64 -0.44 -0.22 0.00 ]
The next blog post will be on July 5 since tomorrow will be the 4th of July (Happy Birthday, United States).
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.