Answer
$r = 3~cos~3\theta$
This graph is a rose curve.
We can see this graph below:
Work Step by Step
$r = 3~cos~3\theta$
When $\theta = 0^{\circ}$, then $r = 3~cos~0^{\circ} = 3$
When $\theta = 20^{\circ}$, then $r = 3~cos~60^{\circ} = 1.5$
When $\theta = 30^{\circ}$, then $r = 3~cos~90^{\circ} = 0$
When $\theta = 60^{\circ}$, then $r = 3~cos~180^{\circ} = -3$
When $\theta = 90^{\circ}$, then $r = 3~cos~270^{\circ} = 0$
When $\theta = 120^{\circ}$, then $r = 3~cos~360^{\circ} = 3$
When $\theta = 180^{\circ}$, then $r = 3~cos~540^{\circ} = -3$
When $\theta = 240^{\circ}$, then $r = 3~cos~720^{\circ} = 3$
When $\theta = 270^{\circ}$, then $r = 3~cos~810^{\circ} = 0$
When $\theta = 300^{\circ}$, then $r = 3~cos~900^{\circ}= -3$
This graph is a rose curve.
We can see this graph below:
