Cartesian equation for a polar curve?

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r=√(x²+y²)
Θ=tan(-1)y/x

r=2sinθ
√(x²+y²=2sin(tan(-1)(y/x))
√(x²+y²=2y/√(x²+y²)
x²+y²=2y
(y-1)²+x²=1

the restriction (0<=θ<π) means only once around the circle so the equation is correct as is....Show more