Chapter 1.1, Problem 58E

For the following exercises, use a graphing utility to graph the curve represented by the parametric equations and identify the curve from its equation.

58. Sketch the curve known as an epitrochoid, which gives the path of a point on a circle of radius b as it rolls on the outside of a circle of radius a. The equations are

   $\begin{array}{l}x=\left(a+b\right)\cos t-c\cdot \cos \left[\frac{\left(a+b\right)t}{b}\right]\\ y=\left(a+b\right)\sin t-c\cdot \sin \left[\frac{\left(a+b\right)t}{b}\right]\end{array}$

Let $a=1,b=2,c=1$ .