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

Jul 7, 2016

${x}^{2} + {y}^{2} = \sqrt{{x}^{2} + {y}^{2}} - y$

#### Explanation:

you have

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

and from that

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

so we have

$\sqrt{{x}^{2} + {y}^{2}} = 1 - \frac{y}{r}$

$\sqrt{{x}^{2} + {y}^{2}} = 1 - \frac{y}{\sqrt{{x}^{2} + {y}^{2}}}$

so time by the radical and you have

${x}^{2} + {y}^{2} = \sqrt{{x}^{2} + {y}^{2}} - y$