PARAMETRIC EQUATIONS

There are many instances where a parametric representation of a function or a curve is preferred, especially in geometric and computer graphics domains.

For example, a point on a circle

can be expressed as ( x, y ). However, to "plot" the circle a sequence of straight line segments would require a sequence of ( x, y ) pairs ordered around the circle to be generated by iteration through appropriate values of x. At each step, solving for y would be necessary from the equation

that must involve two values for each x and a square root calculation

A much simpler solution is to traverse the circle in polar coordinates with

that can be viewed as a set of parametric equations with parameter q.