Answer
$r = 3+cos~\theta$
This graph is a convex limacon.
We can see this graph below:
Work Step by Step
$r = 3+cos~\theta$
When $\theta = 0^{\circ}$, then $r = 3+cos~0 = 4$
When $\theta = 60^{\circ}$, then $r = 3+cos~60^{\circ} = 3.5$
When $\theta = 90^{\circ}$, then $r = 3+cos~90^{\circ} = 3$
When $\theta = 120^{\circ}$, then $r = 3+cos~120^{\circ} = 2.5$
When $\theta = 180^{\circ}$, then $r = 3+cos~180^{\circ} = 2$
When $\theta = 240^{\circ}$, then $r = 3+cos~240^{\circ} = 2.5$
When $\theta = 270^{\circ}$, then $r = 3+cos~270^{\circ} = 3$
When $\theta = 300^{\circ}$, then $r = 3+cos~300^{\circ} = 3.5$
Since $\frac{3}{1}\gt 2$, this graph is a convex limacon.
We can see this graph below:
