# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 395: 49

$r = 3+cos~\theta$ 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:

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