This lab will use Maple to plot and study parametrically defined curves.
The x and y components of the points on the curve are descibed as a function of a parameter t (the independent variable). The set (x(t),y(t)) can be plotted using the plot or ParamPlot commands.
> plot([2*cos(t), 2*sin(t), t = 0..2*Pi]);
will give you the plot of the circle of radius 2 centered at the origin. If you want to use ParamPlot for the same plot, you have to use the following:
> ParamPlot([2*cos(t), 2*sin(t)], t = 0..2*Pi);
Note that the brackets are in a different place.
For obtaining the arc length or area below a curve you need to compute an integral using the formulas in 9.4.
The goal of the exercises is to investigate the general shape associated with certain equations in two and three dimensions. This may be done by varying certain constants within the equations (actually called ``parameters" themselves). Maple is an excellent environment to do this in; once the command works correctly to plot an equation, one may easily change the constants and observe the changes that go along with them, with minimal effort.
On the other hand you must also be aware that theory can help you understand whether the result you obtained using Maple (or any other kind of software) is correct or not.