How do you convert $r = 2cos2θ$ into rectangular form?

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Answer 1 · 2015-12-01T20:18:14

Use these identities:
$x=rcostheta$
$y=rsintheta$
$r^2=x^2+y^2$
$cos2theta=cos^2theta -sin^2theta$

$r=2cos2theta=2[cos^2theta -sin^2theta]$

Now, further simplification using the identities ...

$r=2/r^2(x^2-y^2)=[2(x^2-y^2)]/(x^2+y^2)$

$sqrt(x^2+y^2)=[2(x^2-y^2)]/(x^2+y^2)$

$(x^2+y^2)^(3/2)-2(x^2-y^2)=0$

hope that helps

How do you convert r = 2cos2θr = 2cos2θ into rectangular form?