Parametric curves 

The same plot command that works for curves in the form y=f(x) also works for parametric curves, when both x and y are functions of another independent variable t. 

>	x:= t->cos(t):  y:= t->sin(t):

 

>	plot( [x(t),y(t),t=0..2*Pi] );

 

The result may look like an ellipse instead of a true circle. This is because the two axes can be stretched independently for the display. To make sure that a unit in x always has the same length as a unit in y, you add a special option to the plot (or use a right-click menu on the graph): 

>	plot( [x(t),y(t),t=0..2*Pi], scaling=constrained );

 

Here is the graph of a cycloid (page 690 in Stewart): 

>	plot( [t-sin(t), 1-cos(t), t=0..6*Pi], scaling=constrained);

 

Notice carefully the difference in syntax from the following, which does not give a parametric curve: 

>	plot( [t-sin(t), 1-cos(t)], t=0..6*Pi, scaling=constrained);

 

The following is known as a kind of Lissajous figure. You can see them on old-fashioned oscilloscopes in the backgrounds of some B-movies. 

>	plot( [ sin(3*t+5/2), cos(2*t), t=0..2*Pi ], scaling=constrained );

 

>

 

Polar coordinates 

The most useful aspect of Maple with polar coordinates is in graphing a curve represented by r=f(θ). To use this, load the plots package first. 

>	with(plots):

 

Then, give polarplot the expression f(θ). 

>	polarplot( 2*(1-cos(theta)) );

 

>	polarplot( theta );

 

>	polarplot( 1, scaling=constrained );