Answer
The polar equation of the given polar curve $r=3\sin 2\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 $2n$ number of petals, 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 $4\text{ petals}$, $n$ will be $2$.
And from the graph,
For, $\theta =\frac{\pi }{4}$
$r=3$
And,
For, $\theta =0$
$r=0$
By applying the above condition, we can conclude that the polar equation for the graph will be:
$r=3\sin 2\theta $
