How do you convert $r = 1 - sin (theta)$ into cartesian form?

Question

19929 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-07T12:33:03

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

you have

$x = r cos theta$
$y = r sin theta$

and from that

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

so we have

$sqrt(x^2 + y^2) = 1- y/r$

$sqrt(x^2 + y^2) = 1- y/sqrt(x^2 + y^2)$

so time by the radical and you have

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

How do you convert r = 1 - sin (theta) r = 1 - sin (theta) into cartesian form?