TITLE>Parametric Graphs on Maple

Plotting Parametric Equations with Maple

A point P traces a path in the xy-plane. As P travels, its coordinates x = f(t) and y = g(t) are functions of time. So t is called a parameter, f and g are coordinate functions, and the curve traced out by P is a parametric curve. Maple allows us to graph parametric equations in a way similar to ordinary functions. We use the plot command followed by the parameters enclosed within parentheses.

plot( [ x = f(t), y = g(t), t = range of t ], h, v );

The parameters include

The parametric specifications are a list of three items; the first two are the coordinate functions, f and g, and the third is the range for the parameter, t = range of t .

Ordinary Fuctions

Every ordinary function can be written in parametric form. To produce the sine curve, for example, we can use

x = t; y = sin(t); -2Pi <= t <= 2Pi

The command is

which plots the graph

Circles

The simplest and most important circle is the unit circle which can be written in the xy-form

x^2 + y^2 = 1

or in parametric form

x = cos(t); y = sin(t); 0 <= t <= 2Pi

To plot this circle we use the Maple command

which plots the graph

Other circles may be graphed as well. If (a, b) is any point in the plane, and r > 0 any radius, then the parametric equations

x = a + rsin(t); y = b + rcos(t); 0 <= t <= 2Pi

produce the circle with center (a, b) and radius r.

Experiment by changing the point (a, b) and the radius r to compare the way Maple and your TI-85 graph circles.

Other Curves with Periodic Coordinate Functions

Many curves defined by periodic coordinate functions have striking shapes. Try graphing a Lissajou curve.

Use the command

Replacing the 5 and 6 with other integers produces other Lissajou curves. Also try using t values from 0 to 4Pi.

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Jo Norby-Davis: jnorbyda@nmu.edu.