# How do you convert (-2,-2) into polar form?

Jul 3, 2016

Polar coordinates are $\left(2 \sqrt{2} , \frac{5 \pi}{4}\right)$

#### Explanation:

If $\left(x , y\right)$ are Cartesian coordinates and $\left(r , \theta\right)$ are corresponding polar coordinates, the relation between them is given by $x = r \cos \theta$ and $y = r \sin \theta$.

Hence for point $\left(- 2 , - 2\right)$,

$r = \sqrt{{x}^{2} + {y}^{2}} = \sqrt{{\left(- 2\right)}^{2} + {\left(- 2\right)}^{2}} = \sqrt{4 + 4} = \sqrt{8} = 2 \sqrt{2}$

and $\sin \theta = \cos \theta = 2 \frac{\sqrt{2}}{- 2} = - \frac{1}{\sqrt{2}}$

Hence $\theta = \frac{5 \pi}{4}$

and polar coordinates are $\left(2 \sqrt{2} , \frac{5 \pi}{4}\right)$