Answer
$r = 6-3~cos~\theta$
This graph is a limacon.
We can see this graph below:
Work Step by Step
$r = 6-3~cos~\theta$
When $\theta = 0^{\circ}$, then $r = 6-3~cos~0^{\circ} = 3$
When $\theta = 30^{\circ}$, then $r = 6-3~cos~30^{\circ} = 3.4$
When $\theta = 60^{\circ}$, then $r = 6-3~cos~60^{\circ} = 4.5$
When $\theta = 90^{\circ}$, then $r = 6-3~cos~90^{\circ} = 6$
When $\theta = 120^{\circ}$, then $r = 6-3~cos~120^{\circ} = 7.5$
When $\theta = 180^{\circ}$, then $r = 6-3~cos~180^{\circ} = 9$
When $\theta = 240^{\circ}$, then $r = 6-3~cos~240^{\circ} = 7.5$
When $\theta = 270^{\circ}$, then $r = 6-3~cos~270^{\circ} = 6$
When $\theta = 300^{\circ}$, then $r = 6-3~cos~300^{\circ} = 4.5$
When $\theta = 330^{\circ}$, then $r = 6-3~cos~330^{\circ} = 3.4$
This graph is a limacon.
We can see this graph below:
