Answer
This is a graph of $~~r = a~\theta~~$ for $a=2$ and values of $\theta$ such that $-4\pi \leq \theta \leq 4\pi$
Work Step by Step
This is a graph of $~~r = a~\theta~~$ for $a=2$ and values of $\theta$ such that $-4\pi \leq \theta \leq 4\pi$
Note that $r = 0$ when $\theta = 0$, and the magnitude of $r$ continues to increase as the magnitude of $\theta$ increases. This leads to a spiral shape.
There is symmetry about the vertical axis because both positive and negative values of $\theta$ are included.
At the endpoints of the spiral, $r = 8\pi$ when $\theta = 4\pi$ and the magnitude of $r$ is $8\pi$ when $\theta = -4\pi$
We can see the graph in the window $[-30,30]$ by $[-30,30]$
