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# How do you convert ##r=sin(2theta)## into a cartesian equation?

##x^2 +y^2 =2##

##r = sin (2theta)##

##r = 2sin theta cos theta##

##r = 2(y/r) (x/r) implies r^2 = 2 implies x^2 +y^2 =2##

So it's a circle with radius ##sqrt(2)##.