** 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**

' 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

Notes:

* There are four spaces between PROGRESS: and %. This progress meter is to inform the user of the program's completion.

* The characters % and ', percent sign and apostrophe respectively, are found on the program editing default menu (TOP, BTM, SRC, MENU, A ←→a, CHAR), by pressing [F6] (CHAR), [F2] (SYBL)

* Everything that follows an apostrophe is a comment and can be left out.

* The range of -2π to 2π is used.

* The lower the precision, the faster the graph is made but accuracy of the graph is sacrificed. In a lot of cases, patience is required.

* P is a positive integer.

**Examples**

Example 1: Euler Spiral: A = 1/2, P = 2, precision 32

Example 2: A = 1, P = 3, precision 32

Example 3: A = 2, P = 1, precision 16

Source:

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

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.

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