Question

Test for symmetry with respect to theta=pie/2 , the polar axis, and the pole. with r=16cos3theta

Answer 1

\[r=16 \cos 3 \theta\] and \[\theta=\pi/2\]
Then \[r=16 \cos (3 \pi/2) = 0\]
Since \[\cos (-\theta) = \cos \theta \]
\[r=16 \cos (-3 \pi/2) = 0\]
Therefore, with respect to polar axis, the equation is symmetric about pole.