# 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=25, theta=210^circ?

Mar 4, 2018

Coordinates of color(green)(A = (-(25sqrt3)/2, -25/2)

#### Explanation:

$\vec{O A} = 25 , \theta = {210}^{\circ}$

To find x & y coordinates of point A.

Point A is in third quadrant as $\theta$ is between ${180}^{\circ}$ & ${270}^{\circ}$

Hence, both x , y coordinates are negative.

${A}_{x} = \overline{O A} \cos \theta = 25 \cdot \cos 210 = 25 \cdot \left(- \cos 30\right)$

as $\cos \left(180 + 30\right) = - \cos 30$

${A}_{x} = - \frac{25 \cdot \sqrt{3}}{2}$

${A}_{y} = \overline{O A} \sin \theta = 25 \cdot \sin 210 = 25 \cdot \left(- \sin 30\right)$

as $\sin \left(180 + 30\right) = - \sin 30$

${A}_{y} = - \left(25 \cdot \left(\frac{1}{2}\right)\right) = \frac{25}{2}$

Coordinates of color(green)(A = (-(25sqrt3)/2, -25/2)