Answer
$r=1+4sin\theta$
Work Step by Step
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 $(1,0)$, we have $a=1$
3. Use the point $(5,\frac{\pi}{2})$, we have $a+b=5$, thus $b=4$
4. We have the equation $r=1+4sin\theta$
