# 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=0.5, theta=180^circ?

Apr 7, 2018

$A \left(- 0.5 , \frac{\sqrt{3}}{2}\right)$

#### Explanation:

.

$x$-coordinate of point $A$ is $= O A = 0.5$

$y$-coordinate of point $A$ is $A B$

$\cos \angle A O B = \frac{O A}{O B} = \frac{0.5}{1} = 0.5$

$\angle A O B = \arccos \left(0.5\right) = \frac{\pi}{3}$

$\sin \angle A O B = \frac{A B}{O B} = \frac{A B}{1} = A B$

$\sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$

$A B = \frac{\sqrt{3}}{2}$

Therefore,

$A \left(- 0.5 , \frac{\sqrt{3}}{2}\right)$