# How do you write the cartesian equation for r=1+3sinx?

Jul 9, 2018

As below.

#### Explanation:

$r = 1 + 3 \sin \theta$

$x = r \cos \theta , y = r \sin \theta , r = \sqrt{{x}^{2} + {y}^{2}}$

$\sqrt{{x}^{2} + {y}^{2}} = 1 + 3 \cdot \frac{y}{\sqrt{{x}^{2} + {y}^{2}}}$

${x}^{2} + {y}^{2} = \sqrt{{x}^{2} + {y}^{2}} + 3 y$