Question

What symmetry does the polar curve `r = 3sin3θ` have?

Answer 1

Symmetrical about the pole and, also, #theta = pi/6, theta = (5pi)/6 and theta = (3pi)/2, and also, the radial lines bisecting the angles between these lines..

Explanation:

This is a rose curve with three petals that are 3 units long.

The equispaced lines of symmetry of these petals are `theta=pi/6, theta=(5pi)/6 and theta=(3pi)/2`, respectively.

I think I have exhausted all possibilities, in search of symmetry....