How do you convert $r=7sintheta$ into rectangular equations?

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Answer 1 · 2016-09-16T16:00:31

$x^2+y^2-7y=0$

The relation between polar coordinates $(r,theta)$ and Cartesian coordinates $(x,y)$ is given by

$x=rcostheta$ , $y=rsintheta$ i.e. $x=r/costheta$ , $y=r/sintheta$ and $r^2=x^2+y^2$ ,

Hence $r=7sintheta$ can be written as

$r=7sintheta$ (multiplying both sides by $r$ ) or

$r^2=7rsintheta$ or

$x^2+y^2=7y$ or

$x^2+y^2-7y=0$

graph{x^2+y^2-7y=0 [-10.29, 9.71, -1.48, 8.52]}

How do you convert r=7sinthetar=7sintheta into rectangular equations?