Polar Function Graphs

What AP Precalc asks here

Polar functions have the form $r = f(\theta)$. Three families dominate: circles ($r = a \cos\theta$ or $r = a \sin\theta$), limaçons ($r = a + b \cos\theta$ or $r = a + b \sin\theta$), and roses ($r = a \cos(k\theta)$ or $r = a \sin(k\theta)$ with $k$ controlling the number of petals — $k$ if odd, $2k$ if even).

Look at the form: $a \cos\theta$ alone is a circle; $a + b \cos\theta$ is a limaçon; $\cos(k\theta)$ with $k > 1$ is a rose.

Substitute $\theta$ into $r = f(\theta)$ and use special-angle values.

Plug the candidate $\theta$ into $r = f(\theta)$ and check whether it produces the candidate $r$.