Example: Plotting a Parametric Curve

Plot the curve that is represented parametrically by the equations

and

> plot( [ sin(3*t), sin(4*t), t = 0 .. 2*Pi ] ) ;

To see the direction of the curve, plot it on shorter time intervals, and watch the curve "grow" as you increase the time interval.

> plot( [ sin(3*t), sin(4*t), t = 0 .. 1 ] ) ;

> plot( [ sin(3*t), sin(4*t), t = 0 .. 2 ] ) ;

> plot( [ sin(3*t), sin(4*t), t = 0 .. 3 ] ) ;

> plot( [ sin(3*t), sin(4*t), t = 0 .. 4 ] ) ;

> plot( [ sin(3*t), sin(4*t), t = 0 .. 5 ] ) ;

> plot( [ sin(3*t), sin(4*t), t = 0 .. 6 ] ) ;

> plot( [ sin(3*t), sin(4*t), t = 0 .. 2*Pi ] ) ;

Notice that in this example, the curve begins to trace over itself as we plot it on time intervals that are larger than .