# How do you convert  r = 1 - cos theta into cartesian form?

Dec 6, 2016

The answer is $x + \left({x}^{2} + {y}^{2}\right) = \sqrt{{x}^{2} + {y}^{2}}$

#### Explanation:

To convert from polar coordinates $\left(r , \theta\right)$ to cartesian coordinates, we use the following equations

$x = r \cos \theta$

$y = r \sin \theta$

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

$r = 1 - \cos \theta$

$\cos \theta = 1 - r$

$\frac{x}{r} = 1 - r$

$x = r - {r}^{2}$

$x = \sqrt{{x}^{2} + {y}^{2}} - \left({x}^{2} + {y}^{2}\right)$

$x + \left({x}^{2} + {y}^{2}\right) = \sqrt{{x}^{2} + {y}^{2}}$