# How do you convert (-5, -5) into polar form?

Nov 3, 2016

Cartesian: $\left(x , y\right) = \left(- 5 , - 5\right)$
$\textcolor{w h i t e}{\text{XXX}}$Polar: $\left(r , \theta\right) = \left(5 \sqrt{2} , \frac{5 \pi}{4}\right)$

#### Explanation:

$\left(- 5 , - 5\right)$ is a point in Quadrant III (since both $x$ and $y$ components are negative.

The $x$ and $y$ components are equal, so the reference angle is $\frac{\pi}{4}$.
If the reference angle is $\frac{\pi}{4}$ and the angle is in Q III,
then the angle is $\pi + \frac{\pi}{4} = \frac{5 \pi}{4}$

The radius is the length of the hypotenuse; with an angle of $\frac{\pi}{4}$ the length of the hypotenuse is $\sqrt{2} \times \left\mid \text{length of side} \right\mid$