Answer
To test whether the graph of a polar equation may be symmetric with respect to the line $\theta =\frac{\pi }{2}$ $\left( \text{y-axis} \right)$, replace $\left( r,\theta \right)$ with $\left( -r,-\theta \right)$.
Work Step by Step
When $\left( r,\theta \right)$ is replaced with $\left( -r,-\theta \right)$, if the resultant polar equation is equivalent to given polar equation then a graph of a polar equation exhibits symmetry with respect to the line $\theta =\frac{\pi }{2}$ $\left( \text{y-axis} \right)$.
