Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral

[Eddie W. Shore]

Introduction

The program ESGRAPH plots the parametric equations containing integrals:

x(t) = ∫(cos f(x) dx, x = 0 to t)
y(t) = ∫(sin f(x) dx, x = 0 to t)

The program uses f(x) = a*x^p

When p = 2, the curve is a Euler Spiral (see source).

Casio fx-9750GIII Program: ESGRAPH

Code:


' 2020-12-22 EWS
Rad
' L1, X L2, Y
"F = A×X^P"
"FACTOR"?→A
"P=2, EULER SPIRAL"
"POWER"?→P
∫(A×cos(X^P),0,-2π)→X
∫(A×sin(X^P),0,-2π)→Y
{X}→List 1
{Y}→List 2
Menu "π÷R?","8",A,"16",B,"32",C
Lbl A: 8 → R: Goto 0
Lbl B: 16 → R: Goto 0
Lbl C: 32 → R : Goto 0
Lbl 0
For -2π+π÷R→T To 2π Step π÷R
∫(A×cos(X^P),0,-2π)→X
∫(A×sin(X^P),0,-2π)→Y
Augment(List 1, {X})→List 1
Augment(List 2, {Y})→List 2
(T+2π)÷(4π)×100→G
RndFix(G,0)→G
Locate 1,7,"PROGRESS:    %"
Locate 11,7,G
Next
S-Gph1 DrawOn, xyLine, List 1, List 2, 1, Dot
DrawStat

Havil, Julian. Curves for the Mathematical Curious: An Anthology of the Unpredictable, Historical, Beautiful, and Romantic Princeton Universal Press. Princeton and Oxford. Princeton, NJ 2019 ISBN 978-0-691-18005-2

For examples and more details, visit my blog at Eddie's Math and Calculator blog: http://edspi31415.blogspot.com/2021/01/c...etric.html