Assignment 10

Parametric Equations

by Debra Jackson

In order to understand the results of graphing parametric equations, we must remember and refer to the values on the unit circle from trigonometry, and I have included a copy for easy reference.

In this assignment we are asked to investigate equations x = a cos t and y = b sin t for various values of a and b.

If a = b are equal in value, the result is a circle with various radii as seen in the graph.

If a > b, the result is a circle with various radii as seen in the graph.

If a < b, the result is a circle with various radii as seen in the graph.

The conclusion is that if a > b, the graph is a horizontal ellipse and if a < b the graph is a vertical ellipse.