How do you convert $3 r = sin θ$ $3r=sin theta$ to rectangular form?

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Answer 1 · 2016-11-23T08:34:40

$3 x^{2} + 3 y^{2} - y = 0$ $3x^2+3y^2-y=0$

for polars

$r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$

$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$

$3 r = sin θ$ $3r=sintheta$

multiply both sides by $r$ $""r$

$3 r^{2} = r sin θ$ $3r^2=rsintheta$

substitute in

3(x^2+y^2)=y#

$3 x^{2} + 3 y^{2} - y = 0$ $3x^2+3y^2-y=0$

How do you convert 3r=sin theta3r=sinθ 3r=sin theta to rectangular form?