# How do you find the polar coordinates of the rectangular point (-4,-4)?

Jan 11, 2016

The point #(-4,-4) is in Quadrant III

#### Explanation:

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

Now, the reference angle in Quadrant III is ...

reference angle $= {\tan}^{1} \left(\frac{4}{4}\right) = {45}^{0}$

$\theta = {180}^{o} + {45}^{o} = {225}^{o}$

polar coordinate $\left(r , \theta\right) = \left(4 \sqrt{2} , {225}^{o}\right) = \left(3 \sqrt{2} , \frac{5 \pi}{4}\right)$

hope that helped