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algebraically identify the symmetries of r=2sin(2theta)

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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
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