How do you convert $r^2 = sin 2(theta)$ into cartesian form?

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Answer 1 · 2017-04-21T11:42:08

The equation is $(x^2+y^2)^2=2xy$

To convert from polar coordinates $(r,theta)$ to cartesian coordinates $(x,y)$ , we apply the following equations

$sintheta=y/r$

$costheta=x/r$

$x^2+y^2=r^2$

$Sin(2theta)=2sinthetacostheta$

The equation is

$r^2=sin(2theta)$

$r^2=2sinthetacostheta$

$r^2=2*y/r*x/r$

$r^4=2xy$

$(x^2+y^2)^2=2xy$

How do you convert r^2 = sin 2(theta)r^2 = sin 2(theta) into cartesian form?