# How do you graph the polar equation r=-3sintheta?

May 28, 2018

please show the graph below

#### Explanation:

As $r = - 3 \sin \theta$ ,at $\theta = 0 , \frac{\pi}{4} , \frac{\pi}{2} , \frac{3 \pi}{4} \mathmr{and} \pi$

$r$ takes values $r = 0 , \frac{- 3}{\sqrt{2}} , - 3 , \frac{- 3}{\sqrt{2}} , 0$

Thus these represents points $\left(0 , 0\right) , \left(\frac{- 3}{\sqrt{2}} , \frac{\pi}{4}\right) , \left(- 3 , \frac{\pi}{2}\right) , \left(\frac{- 3}{\sqrt{2}} , 3 \frac{\pi}{4}\right) , \left(0 , \pi\right)$

We can select more such points, say by having$\theta = \frac{\pi}{6} , \frac{\pi}{3} , \frac{2 \pi}{3} , \frac{5 \pi}{6}$

the graph will be appear as follow:

it is a circle with center $\left(- \frac{3}{2} , - \frac{\pi}{2}\right)$ and radius $r = 3$

as $r = - 3 \sin \theta$ it means ${r}^{2} = - 3 r \sin \theta$

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