Curves defined by Parametric Equations.

The equations

define a curve parametrically. For each in the interval , the point is a point on the curve.

In Maple, a curve can be plotted using the command plot and specifying the parameter

as the function to be plotted.

> plot([cos(t),sin(t),t=0..Pi]);

If desired two additional parameters designating the range of the x's and the range of the y's can be added.

> plot([cos(t),sin(t),t=0..Pi],x=-2..2,y=-1..2);

A function such as can be drawn parametrically as follows

> plot([x,x^2,x=-2..2]);

Several curves can be drawn on the same set of axes, by listing them in curly braces.

> plot({[cosh(t),sinh(t),t=-2..2],[-cosh(t),sinh(t),t=-2..2],[t,t,t=-3..3]},x=-2..2,y=-2..2);

Here are some other interesting examples for you to try.

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

> plot([t+2*sin(2*t),t+2*cos(5*t),t=-2*Pi..2*Pi]);

> plot([2*(theta-sin(theta)),2*(1-cos(theta)),theta=0..5*Pi],x=0..31,y=0..15,title="cycloid");