# How do you convert r = 3sin(theta) into a cartesian equation?

Sep 22, 2015

Use $r = \sqrt{{x}^{2} + {y}^{2}}$ and $\sin \left(\theta\right) = \frac{y}{r}$ to get:

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

#### Explanation:

$r = \sqrt{{x}^{2} + {y}^{2}}$ and $\sin \left(\theta\right) = \frac{y}{r}$

So $r = 3 \sin \left(\theta\right)$ becomes:

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

Multiply both sides by $\sqrt{{x}^{2} + {y}^{2}}$ to get:

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

graph{x^2+y^2-3y=0 [-4.913, 5.087, -0.98, 4.02]}