- r=2/1+sin (- u), solve for and cofirm if it is the same as r=2/1+sinu

Question

Testing for symmetry in respect to theta=pi/2, the polar axis, and the pole. Used original equation r=2/1+sinu, then substituted -r and - u to test symmetry about thrta = pi/2.

Answer 1

The function is periodic. Symmetry is about 2nπ+π/2, a minimum point, r=1, not the vertical axis (u=0). When u=nπ where n is an integer, r=2. There are asymptotes at 2nπ-π/2. Halfway between asymptotes is a line of symmetry: ½(2nπ-π/2+2(n+1)π-π/2)=½(4nπ+π)=2nπ+π/2.