# A circle has a centre at the point [3, pi/2] in polar coordinates and a radius of 3. How do you find the equation of the circle in polar notation?

Jan 10, 2017

#### Explanation:

When given a polar point, $\left({r}_{0} , \phi\right)$, and a radius R.

The reference says that the equation of a circle in polar form is:

${r}^{2} - 2 {r}_{0} \cos \left(\theta - \phi\right) r + r {o}^{2} = {R}^{2}$

Let's substitute the values for this problem:

$R = 3 , {r}_{0} = 3 , \mathmr{and} \phi = \frac{\pi}{2}$

${r}^{2} - 2 \left(3\right) \cos \left(\theta - \frac{\pi}{2}\right) r + {3}^{2} = {3}^{2}$

${r}^{2} - 6 \cos \left(\theta - \frac{\pi}{2}\right) r = 0$

${r}^{2} = 6 \cos \left(\theta - \frac{\pi}{2}\right) r$

$r = 6 \sin \left(\theta\right)$