# Math Help - polar coordinates

1. ## polar coordinates

Determine the main set of polar coordinates of points which are rectangular coordinates:

$(0,-2)$

$p=\sqrt{0^2+(-2)^2}$
$p=+or-2$

How do I find the angle?

$(2,270°)$

2. Hi Apprentice123,

Given the coordinates $(a,b)$ the angle $(\theta)$ is given by $\arctan\left(\frac{b}{a}\right)$ Thus in this case $\theta=\arctan\left(\frac{-2}{0}\right)$ Note two things. The first is that $\frac{-2}{0}$ is undefined so we want $\theta$ such that $\tan(\theta)$ is undefined. The second is that the coordinates $(0,-2)$ are in the fourth quadrant and thus so is your angle.

        |
* (0, -2)
We see that the angle is $\frac{3\pi}{2}$ away from the polar axis.