# How do you convert r= 2 sin r + 2 cos r into cartesian form?

Sep 28, 2016

Perhaps, the equation is $r = 2 \left(\sin \theta + \cos \theta\right)$. If so, the cartesian form is ${\left(x - 1\right)}^{2} + {\left(y - 1\right)}^{2} = 2$.

#### Explanation:

I solve this for the corrected version $r = 2 \left(\sin \theta + \cos \theta\right)$

The conversion equation is r)cos theta, sin theta ) = (x, y) that

gives ) $r = \sqrt{{x}^{2} + {y}^{2}} \ge 0$, for the principal value,

$\sin \theta = \frac{y}{\sqrt{{x}^{2} + {y}^{2}}} \mathmr{and} \cos \theta = \frac{x}{\sqrt{{x}^{2} + {y}^{2}}}$

Here,

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

Cross multiplying and reorganizing,

${\left(x - 1\right)}^{2} + {\left(y - 1\right)}^{2} = 2$