Explain why the following test for symmetry is valid: Replace r by -r and by -

Explain why the following test for symmetry is valid: Replace r by -r and θ by -θ in a polar equation. If an equivalent equation results, the graph is symmetric with respect to the line θ = π/2 (y-axis).

(a)  Show that the test fails for  r² = cosθ yet this new test works.

(b) Show that the test works for r² = sinθ yet this new test fails.