Answer
To test the symmetry with respect to the line, replace $\left( r,\theta \right)$ with $\left( -r,-\theta \right)$, if the resultant equation is equivalent to the given equation, then the graph is symmetric with respect to $\theta =\frac{\pi }{2}$.
Work Step by Step
For example:
We will replace $\left( r,\theta \right)\,\text{with}\,\left( -r,-\theta \right)$ in the polar equation $r=1-2\cos \theta $ to perform the test for the line $\theta =\frac{\pi }{2}$,
$\begin{align}
& r=1-2\cos \theta \\
& -r=1-2\cos \left( -\theta \right) \\
& -r=1-2\cos \theta
\end{align}$
The resultant equation changes and thus it fails this symmetry test.
