## Precalculus (6th Edition) Blitzer

The polar equation of the given polar curve is $r=3\sin 3\theta$.
From the given polar curve we can observe that it is a rose curve. In case of a rose curve of $n$ number of petals (where $n$ is odd), the general form of the polar equation will be either $r=a\sin n\theta$ or $r=a\cos n\theta$, $a>0$. Hence, for $\text{3 petals}$, $n$ will be $3$. And on the basis of the graph, For, $\theta =\frac{\pi }{6}$ $r=3$ And, For, $\theta =0$ $r=0$ By applying the above condition, it is concluded that the polar equation for the graph will be $r=3\sin 3\theta$.