How do you convert $r^2=sin2(theta)$ to rectangular form?

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Answer 1 · 2016-02-08T01:18:27

Use the following identities:

$sin2theta=2costhetasintheta$
$x=rcostheta$
$y=rsintheta$
$x^2+y^2=r^2$

Using the above identities ...

$r^2=sin2(theta)$

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

Now simplify ...

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

$x^4+2x^2y^2+y^4-2xy=0$

hope that helped

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How do you convert r^2=sin2(theta)r^2=sin2(theta) to rectangular form?