Fun with the TI-73 Part II: Rolling Two Dice, Numerical Derivative, Rectangular/Polar Conversions
TI-73 Program: TWODICE - Rolling Two Dice
Introduction:
The program TWODICE will roll two regular dice and give the sum of those dice in three lists:
L_1: die 1
L_2: die 2
L_3: total
If there are seven rolls or less, the program displays the rolls. In any case, the results are stored in the above lists.
Access L_1 by pressing [ 2nd ] [ STAT ] (LIST), 1
Access L_2 by pressing [ 2nd ] [ STAT ] (LIST), 2
Access L_3 by pressing [ 2nd ] [ STAT ] (LIST), 3
Program:
"EWS 2021"
Disp "ROLL THE DICE"
Input "ROLLS? ",X
dice(X)→L_1
dice(X)→L_2
L_1+L_2→L_3
If X≤7
Then
ClrScreen
For(A,1,X)
Output(A,1,L_1(A))
Output(A,3,L_2(A))
Output(A,6,L_3(A))
End
Pause
End
ClrScreen
Disp "L_1 = DIE 1","L_2 = DIE 2","L_3 = TOTAL"
Pause
Your results will vary.
TI-73 Program: DERIVY1 - Numerical Derivative of y1(x)
The simple program DERIVY1 calculates the numerical derivatives of the equation stored in Y_1.
Access Y_1 by pressing [ 2nd ] [ APPS ] (VARS), 2, 1
Program:
"EWS 2021"
Disp "D/DX Y_1"
Prompt X
10^(-8)→H
(2*H)^-1*(Y_1(X+H)-Y_1(X-H))→D
Disp "APPROX D/DX"
Pause D
Example:
Y_1 = (X^2-3)^2 + 1
Derivative at x = 0.95, Result: -7.9705
Derivative at x = 2, Result: 8
Y_1 = e^(X^3/4)
Derivative at x = 0.46, Result: 0.16261
Derivative at x = 1.55, Result: 4.571295
TI-73 Program: RECPOL - Rectangular/Polar Conversion
This program has two conversions:
1. >RECT: Polar (r, θ) to Rectangular (x, y)
2. >POLAR: Rectangular (x, y) to Polar (r, θ)
This program works in either Degree or Radian mode.
I take a different approach to calculate angle than the atan2 method. Approached this as calculating the angle between the vectors [ x, 0 ] and [ x, y]. The angle between vectors v1 and v2 is:
θ = acos( dot(v1, v2) / ( norm(v1) * norm(v2) ) = acos( x / √(x^2 + y^2))
The angle is negative if y<0.
Like the argument and angle conversions, the point (0,0) is defined to have an angle of 0.
Since there is no theta character (θ) on the TI-73, I use the variable A instead.
Program:
"EWS 2021"
Lbl 0
Menu("MENU",">RECT",1,">POLAR",2,"EXIT",3)
Lbl 1
Input "R? ",R
Input "ANG? ",A
R*cos(A)→X
R*sin(A)→Y
Disp "X= ",X,"Y= ",Y
Pause
Goto 0
Lbl 2
Input "X? ",X
Input "Y? ",Y
√(X^2+Y^2)→R
If X=0 and Y=0
Then
0→A
Else
cos^-1(X/√(X^2+Y^2))→A
If Y<0
-A→A
End
Disp "R=",R,"ANG=",A
Pause
Goto 0
Lbl 3
Examples:
Examples are in Degree mode.
R = 19, ANG = 87.3°
Result: X = 0.8950225635, Y = 18.97890762
X = -11.5, Y = 2.4
Result: R = 1.74776575, ANG = 168.2118167
Eddie
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