** 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

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