Answer
The polar equation of the given polar curve is $r=3\sin 3\theta $.
Work Step by Step
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 $.
