# How do you find the polar coordinates of (-4,0) ?

Sep 20, 2014

The rectangular coordinates $\left(x , y\right) = \left(- 4 , 0\right)$ is equivalent to the polar coordinates $\left(r , \theta\right) = \left(4 , \pi\right)$

Let us look at some details.

Since $r$ is the distance of $\left(- 4 , 0\right)$ from the origin,

$r = \sqrt{{\left(- 4\right)}^{2} + {0}^{2}} = 4$

Since the segment from the origin to $\left(- 4 , 0\right)$ makes ${180}^{\circ} = \pi$ rad with the positive x-axis,

$\theta = \pi$