Find symmetry of the polar equation r = 3 sin 2θ?

Question

Find symmetry at the pole, the line π/2 or the polar axis of the polar equation r = 3 sin 2θ and r = 4 cos 3θ.

For r = 3 sin 2θ I got only the line π/2, but according to the book it is also symmetric along the polar axis and the pole. I don't understand this because (r, θ) ≠ (r, -θ) and (-r, θ) ≠ (r, θ).

Answer 1

r = 3sin(2θ) is 4-petaled and exhibits point symmetry about the origin (r(θ) = r(θ + 180), as well as about the lines θ = 0, θ = π/4, θ = π/2, and θ = 3π/4.

r = 4cos(3θ) is 3-petaled and is symmetrical about the lines θ = 0, θ = π/6, and θ = π/3.

(r, θ) = (-r, θ + 180)

(-r, θ) = (r, θ + 180)

so

(-4, 45°) = (4, 225°)