How do you convert $r^2 = sin2t$ into a rectangular equation?

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Answer 1 · 2018-03-04T16:24:07

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

Th relation between polar coordinates $(r,theta)$ and rectangular coordinates $(x,y)$ is given by

$x=rcostheta$ , $y=rsintheta$ and hence $sintheta=y/r$ , $costheta=x/r$ and $x^2+y^2=r^2$

Hence, we can write $r^2=sin2theta=2sinthetacostheta$ as

$x^2+y^2=2(xy)/(x^2+y^2)$ - as in denominator we have $r^2=x^2+y^2$

and therefore our equation in rectangular form is

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

graph{(x^2+y^2)^2=2xy [-2.5, 2.5, -1.25, 1.25]}

How do you convert r^2 = sin2tr^2 = sin2t into a rectangular equation?