Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 389: 42

graph D

$r = cos~3\theta$ When $\theta = 0^{\circ}$, then $r = cos~2\theta = 1$ When $\theta = 30^{\circ}$, then $r = cos~2\theta = 0$ When $\theta = 60^{\circ}$, then $r = cos~2\theta = -1$ When $\theta = 90^{\circ}$, then $r = cos~2\theta = 0$ When $\theta = 120^{\circ}$, then $r = cos~2\theta = 1$ We can see that this matches up with graph D.