# What is the polar form of ( -10,22 )?

Jun 17, 2017

(2sqrt146,1.998 "rad")

#### Explanation:

The polar form of the rectangular coordinate $\left(x , y\right)$ can be found using these formulas:

$r = \sqrt{{x}^{2} + {y}^{2}}$
$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$

So let's plug in the given x and y values.

$r = \sqrt{{\left(- 10\right)}^{2} + {22}^{2}} = \sqrt{100 + 484} = \sqrt{584} = 2 \sqrt{146}$

$\theta = {\tan}^{-} 1 \left(\frac{22}{-} 10\right) = - 1.144$ $r a d$

Now, since this point is in quadrant 2, and the angle produced by ${\tan}^{-} 1 \left(\frac{y}{x}\right)$ is in quadrant 4, we need to add $\pi$ $r a d$ to $\theta$ to get the correct angle.

So our polar coordinates are:

$\left(2 \sqrt{146} , 1.998\right)$