How do you convert $r^ 2 = 2 sin 2θ$ to rectangular form?

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Answer 1 · 2016-09-21T04:39:49

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

Use the conversions
$r^2=x^2+y^2$
$x=rcostheta$ or $costheta=x/r$
$y=rsintheta$ or $sintheta=y/r$

$r^2=2sin(2theta)$

$r^2=2(2sinthetacostheta)color(white)(aaa)$ Use the identity $sin2theta=2sinthetacostheta$
$r^2=4sinthetacostheta$

$x^2+y^2=4sinthetacosthetacolor(white)(aaaa)$ Substitute $x^2+y^2$ for $r^2$

$x^2+y^2=4*y/r*x/rcolor(white)(aaaaa)$ Substitute $y/r$ for $sintheta$ and $x/r$ for $costheta$

$x^2+y^2=(4xy)/r^2$

$x^2+y^2=(4xy)/(x^2+y^2)color(white)(aaaaaa)$ Substitute $x^2+y^2$ for $r^2$

$(x^2+y^2)^2=4xycolor(white)(aaaaaaa)$ Multiply both sides by $(x^2+y^2)$

How do you convert r^ 2 = 2 sin 2θ r^ 2 = 2 sin 2θ to rectangular form?