Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
01-10-2021, 04:17 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,290 Joined: Dec 2013
Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral
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
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 Messages In This Thread Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Eddie W. Shore - 01-10-2021 04:17 PM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Hlib - 01-14-2021, 04:30 PM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Eddie W. Shore - 01-16-2021, 03:15 PM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Nad - 01-17-2021, 03:34 AM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - EdS2 - 01-17-2021, 08:29 AM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Benjer - 01-17-2021, 06:56 PM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - davej - 01-17-2021, 07:49 PM RE: Casio fx-9750GIII: Trigonometric Integral Graphs, including The Euler Spiral - Steve Simpkin - 01-17-2021, 08:16 PM

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