algebraically identify the symmetries of r=2sin(2theta)
sin2θ = 2sinθcosθ
sin(θ+π/2) = cosθ
cos(θ+π/2) = -sinθ
play around with that some, and verify your algebra with the graph:
http://www.wolframalpha.com/input/?i=plot+r%3D2sin2%CE%B8
sin(θ+π/2) = cosθ
cos(θ+π/2) = -sinθ
play around with that some, and verify your algebra with the graph:
http://www.wolframalpha.com/input/?i=plot+r%3D2sin2%CE%B8