Chapter 8 - Polar Coordinates; Vectors - Section 8.2 Polar Equations and Graphs - 8.2 Assess Your Understanding - Page 607: 69

$r=4+sin\theta$

1. Based on the given graph, we can see that the symmetry axis is vertical and we can select the model $r=a+b\ sin\theta$ 2. Use the point $(4,0)$, we have $a=4$ 3. Use the point $(5,\frac{\pi}{2})$, we have $a+b=5$, thus $b=1$ 4. We have the equation $r=4+sin\theta$