How do you convert $r = 1 + 2 sin theta$ to rectangular form?

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Answer 1 · 2018-03-12T08:48:49

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

Multiply each term by $r$ to get $r^2=r+2rsintheta$

$r^2=x^2+y^2$
$r=sqrt(x^2+y^2)$
$2rsintheta=2y$

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

$x^2+y^2-2y=sqrt(x^2+y^2)$

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

How do you convert r = 1 + 2 sin thetar = 1 + 2 sin theta to rectangular form?