How do you convert $r=sin2(theta)$ in rectangular form?

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Answer 1 · 2018-05-13T14:45:13

$(x^2 + y^2 ) ^3 = 4x^2y^2$

$r = sin2theta$

$=> r = 2sintheta costheta$

We know $rcos theta = x$

$=> cos theta = x / r = x / ( sqrt(x^2 + y^2 )$

$=> sqrt(x^2 + y^2) = 2 * x/sqrt(x^2 +y^2) * y/sqrt(x^2 + y^2 )$

$=> sqrt(x^2 + y^2 ) = (2xy)/(x^2 + y^2 )$

$=> (x^2 + y^2) ^ (3/2) = 2xy$

$=> (x^2 + y^2 ) ^3 = 4x^2y^2$

How do you convert r=sin2(theta) r=sin2(theta) in rectangular form?