Writing Polar Equations In Parametric Form For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\cos 3\theta$, and re-wrote it as the parametric equations $x=2\cos 3\theta \cos \theta$ and $y=2\cos 3\theta \sin \theta$. How did the author arrive at these parametric equations?

Hint: Use this fact that there is a transformation from Cartesian coordinate to Polar coordinate: $$x=r\cos(\theta), y=r\sin(\theta),\;\; r>0\;\;\text{and}\;\; \theta\in[0,2\pi]$$
