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?

Generaly if $r(\theta)$ is the polar function, the cartesian coordinates are given by $x(\theta)=r(\theta)\cos \theta$ and $y(\theta)=r(\theta)\sin \theta$. These are your parametric equations.
