# How do you plot the point (-3,-150^o) on a polar graph?

Dec 23, 2017

see explanation.

#### Explanation:

$- {150}^{\circ}$ is coterminal to ${210}^{\circ}$, so locate ${210}^{\circ}$ on your coordinate plane. It's ${30}^{\circ}$ past ${180}^{\circ}$ in the counterclockwise direction. Imagine standing at the origin facing ${210}^{\circ}$. If $r$ is positive you would walk forward into QIII but since $r$ is negative you're going to walk backward into QI. Walk 3 units backward into QI. This is equivalent to facing ${30}^{\circ}$ and walking forward 3 units so another representation of this point is $\left(3 , {30}^{\circ}\right)$.

Since we can convert polar to rectangular, we can also find the rectangular point:

$x = r \cdot \cos \left(\theta\right)$
$x = - 3 \cos \left({210}^{\circ}\right) = - 3 \left(- \frac{\sqrt{3}}{2}\right) = \frac{3 \sqrt{3}}{2}$

$y = r \cdot \sin \left(\theta\right)$
$y = - 3 \sin \left({210}^{\circ}\right) = - 3 \left(- \frac{1}{2}\right) = \frac{3}{2}$

So you end up at the point $\left(\frac{3 \sqrt{3}}{2} , \frac{3}{2}\right)$