Answer
$r = 3~cos~5\theta$
This graph is a rose.
We can see this graph below:
Work Step by Step
$r = 3~cos~5\theta$
When $\theta = 0^{\circ}$, then $r = 3~cos~0^{\circ} = 3$
When $\theta = 6^{\circ}$, then $r = 3~cos~30^{\circ} = 2.60$
When $\theta = 9^{\circ}$, then $r = 3~cos~45^{\circ} = 2.12$
When $\theta = 12^{\circ}$, then $r = 3~cos~60^{\circ} = 1.5$
When $\theta = 18^{\circ}$, then $r = 3~cos~90^{\circ} = 0$
When $\theta = 30^{\circ}$, then $r = 3~cos~150^{\circ} = -2.60$
When $\theta = 36^{\circ}$, then $r = 3~cos~180^{\circ} = -3$
When $\theta = 48^{\circ}$, then $r = 3~cos~240^{\circ} = -1.5$
When $\theta = 54^{\circ}$, then $r = 3~cos~270^{\circ} = 0$
When $\theta = 60^{\circ}$, then $r = 3~cos~300^{\circ} = 1.5$
When $\theta = 72^{\circ}$, then $r = 3~cos~360^{\circ} = 3$
When $\theta = 90^{\circ}$, then $r = 3~cos~450^{\circ} = 0$
When $\theta = 108^{\circ}$, then $r = 3~cos~540^{\circ} = -3$
When $\theta = 126^{\circ}$, then $r = 3~cos~630^{\circ} = 0$
When $\theta = 144^{\circ}$, then $r = 3~cos~720^{\circ} = 3$
When $\theta = 162^{\circ}$, then $r = 3~cos~810^{\circ} = 0$
When $\theta = 180^{\circ}$, then $r = 3~cos~900^{\circ} = -3$
For larger values of $\theta$, the points on the graph are repeated.
This graph is a rose.
We can see this graph below:
