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Identify the curve by finding a cartesian equation for the curve r^2 sin 2 theta=1

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The answer is
2xy = 1


The transformation between polar and cartesian coordinates is



r = √(x^2+y^2),\qquad r\sin(\theta)=y,\qquad r\cos(\theta)=x


Now use the trigonometric identity
\sin(2\theta)=2\sin(\theta)\cos(\theta) to rewrite the expression as



r^2\sin(2\theta) = 2r^2\sin(\theta)\cos(\theta) = 2r\sin(\theta)r\cos(\theta)


Now recall the transformations to rewrite



2r\sin(\theta)r\cos(\theta) = 2xy

User SethO
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