Question

To test if the graph of a polar equation may be symmetric with respect to the line$\theta =\frac{\mathrm{\pi }}{2},$replace $\theta$by ______.

Short answer

To test if the graph of a polar equation may be symmetric with respect to the line $\theta =\frac{\mathrm{\pi }}{2},$replace $\theta$by$\pi -\theta .$

Step-by-step solution

Step 1. Given Information  

We have to fill the blank for the given statement "To test if the graph of a polar equation may be symmetric with respect to the line $\theta =\frac{\mathrm{\pi }}{2},$replace $\theta$by _____".

Step 2. Filling the blank

To test if the graph of a polar equation may be symmetric with respect to the line$\theta =\frac{\mathrm{\pi }}{2},$replace $\theta$by$\pi -\theta .$