Chapter 10.7, Problem 72SE

For the following exercises, look at the graphs of each of the four parametric equations. Although they look unusual and beautiful, they are so common that they have names, as indicated in each exercise. Use a graphing utility to graph each on the indicated domain.

72. An hypotrochoid: $\{\begin{array}{l}x\left(t\right)=2\sin t+5\cos \left(6t\right)\\ y\left(t\right)=5\cos t-2\sin \left(6t\right)\end{array}$ on the domain $\left[0,2\pi \right]$ .