# What is the polar form of ( 0,-9 )?

Dec 6, 2015

$9 \angle - \frac{\pi}{2}$

#### Explanation:

Any point $\left(x , y\right)$ in rectangular form may be converted into polar form $\left(r , \theta\right)$ as follows

$r = \sqrt{{x}^{2} + {y}^{2}}$

$\theta = {\tan}^{- 1} \left(\frac{y}{x}\right)$

Where $\theta$ is always measured anti-clockwise from the positive x-axis.

So in this case, $r = \sqrt{{0}^{2} + {9}^{2}} = 9$

Since this point $\left(0 , - 9\right)$ lies on the negative y-axis, its angle from the positive x-axis is $- {90}^{\circ} \mathmr{and} - \frac{\pi}{2}$ radians