Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 396: 78

This is a graph of $~~r = a~\theta~~$ for $a=-1$ and values of $\theta$ such that $0 \leq \theta \leq 12\pi$

This is a graph of $~~r = a~\theta~~$ for $a=-1$ and values of $\theta$ such that $0 \leq \theta \leq 12\pi$ 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. At the endpoint of the spiral, the magnitude of $r$ is $36\pi$ when $\theta = 12\pi$ We can see the graph in the window $[-40,40]$ by $[-40,40]$