# How do you graph r=2sintheta?

Apr 8, 2018

#### Explanation:

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

$r$ takes the values $0 , \sqrt{2} , 2 , \sqrt{2} , 0$

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

We can select more such points, say by having $\theta = \frac{\pi}{6} , \frac{\pi}{3} , \frac{2 \pi}{3} , \frac{5 \pi}{6}$ and corresponding value of $r$ would be $r = 1 , \sqrt{3} , \sqrt{3} , 1$ and points are $\left(1 , \frac{\pi}{6}\right)$, $\left(\sqrt{3} , \frac{\pi}{3}\right)$, $\left(\sqrt{3} , \frac{2 \pi}{3}\right)$ and $\left(1 , \frac{5 \pi}{6}\right)$.

The gaph will appear as follows:

It is a circle with center at $\left(1 , \frac{\pi}{2}\right)$ and radius $1$

and as $r = 2 \sin \theta$ means ${r}^{2} = 2 r \sin \theta$

in rectangular coordinates, it is equivalent to ${x}^{2} + {y}^{2} = 2 y$