# How do you convert r = 8 sin θ into rectangular equations?

Feb 8, 2016

${x}^{2} + {y}^{2} = 8 y$

#### Explanation:

using : y = $r \sin \theta \Rightarrow \sin \theta = \frac{y}{r}$

then r $= \frac{8 y}{r}$

( multiply both sides by r )

hence : ${r}^{2} = 8 y$

(now using ${r}^{2} = {x}^{2} + {y}^{2}$)

$\Rightarrow {x}^{2} + {y}^{2} = 8 y$