To use the Parametric Curves utility, choose the command "Parametric Curves" from the Utilities Menu. The menu bar will disappear, and the parametric curves utility will fill the screen. This utility allows you to easily draw the graph of one or more parametric curves of the form (x(t),y(t)) for t ranging between a starting value and a stopping value which you can specify.
Simply enter formulas for the two functions x(t) and y(t) in the text-entry rectangles on the bottom of the screen. Note that these functions must be expressed in terms of the variable t, not x. You can also assign new values to xmin, xmax, ymin, and ymax, which determine the portion of the xy-plane that will be represented on the screen. You can specify the starting value and the final value for t, and you can specify a value for "delta T". (See below.) When you click on the Graph button, the curve will be drawn. You can draw up to 25 curves at a time; after that, you will have to Clear before proceeding. There is a check box that you can check if you want the graph to be cleared automatically before each curve is drawn.
When a curve is to be drawn, it is generated as follows: The numbers t0, t1, ..., tN are generated beginning with the start value for t. The difference between consecutive numbers in this list is given by delta T. The numbers are generated until the specified final value of t has been passed. For each of the numbers ti, the values of the functions x(ti) and y(ti) are computed. The points (x(t1),y(t1)), (x(t2),y(t2)), ..., x(tN),y(tN)) are plotted, with line segments between consecutive pairs of points. Assuming that delta T is small enough, you will get a good approximation of the parametric curve (x(t),y(t)).
Note that the drawing procedure is not very intelligent: If delta T is too big, you will not get a decent picture of the details of the curve. If the curve wanders outside of the specified ranges of x and y, only the part inside those ranges will be visible--no way is provided to automatically scale the screen to fit the curve. Worst of all, if the curve is discontinuous, it will probably be incorrectly drawn as if it were continuous.
