**Parametric Curve Plotting in Maple**

**Copyright © 1999 , 2002by James F. Hurley, University of Connecticut Department of Mathematics, Unit 3009, Storrs CT 06269-3009. All rights reserved.**

Maple has a simple command to generate a plot of parametric equations

* x*
=
*x(t) = f(t), y = y(t) = g(t), t*
* Î*
[
*a, b*
].

Its syntax is

plot( [ x(t), y(t), t = a..b ] ) .

For example, the following simple command plots the circle of radius 4 centered at the origin. To execute it, recall that you place the cursor after the semicolon, and hit the Enter key.

`> `
**plot( [ 4*cos(t), 4*sin(t), t = 0..2*Pi ] );
**

Notice that, rather than circular, the plot appears elliptical. To correct that, add the command
scaling = constrained
, which instructs Maple to use the same scaling on each coordinate axis. Execute the following command to see the effect.

`> `
**plot( [ 4*cos(t), 4*sin(t), t = 0..2*Pi ], scaling = constrained );
**

To polish the plot still more, add a title and labels along the coordinate axes. Maple allows you to specify the font for a title, but you must use UPPER CASE letters in the specification. Try it!

`> `
**plot( [ 4*cos(t), 4*sin(t), t = 0..2*Pi ], scaling = constrained, title = "Plot of Circle", titlefont = [HELVETICA, BOLD, 18], labels = ["x", "y"] );
**

The next command plots the parametric equations
as
*t*
varies over the interval [0, 10], parametric equations from Exercise 6 of Section 11.1 of Stewart's
*Calculus, 4th Ed*
. In this case, constrained scaling is not specified, because the coordinate values differ in size by an order of magnitude so equal scales on each axis would produce a plot whose height would be out of proportion to its width.

`> `
**plot( [ t^2, t^3, t = 0..10 ], title = "Plot of Ex. 6, p.679", titlefont = [HELVETICA, BOLD, 18], labels = ["x", "y"] );
**

As a concluding example, consider the more complicated command below, which plots the graph of a hypocycloid of 59 cusps centered at the origin. Execute it to see an interesting plot.

`> `

`> `
**plot( [42*cos(t) + 17*cos(42*t/17), 42*sin(t) - 17*sin(42*t/17), t = 0..34*Pi ], scaling = constrained, title = "Plot of a Hypocycloid of 59 cusps", titlefont = [HELVETICA, BOLD, 18],labels = ["x", "y"] );
**

`> `

Maple's simple, intuitive command structure for parametric plotting makes it a very convenient tool to generate quick and accurate plots. Since it is important to become familiar with making plots manually, use it to check simple hand-generated plots. For curves like the last one, for which hand plotting is inadequate, the computer provides a convenient way to generate accurate images.