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
All original content copyright, © 2011-2021. 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.
