# How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is theta: OA=8, theta=120^circ?

##### 1 Answer
Mar 6, 2018

Coordinates of color(blue)(A (-4, 4 sqrt3)

#### Explanation:

${120}^{\circ}$ is in second quadrant

${A}_{x} = \overline{O A} \cdot \cos \theta = 8 \cdot \cos 120 = 8 \cdot \left(- \cos \left(60\right)\right) = 8 \cdot - \left(\frac{1}{2}\right) = - 4$

$\textcolor{b l u e}{{A}_{x} = - 4}$

${A}_{y} = \overline{O A} \cdot \sin \theta = 8 \cdot \sin 120 = 8 \cdot \sin 60 = 8 \cdot \left(\frac{\sqrt{3}}{2}\right)$

color(blue)(A_y = 4 sqrt3