# 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=sqrt3, theta=300^circ?

Mar 4, 2018

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

#### Explanation:

Given $\theta = {300}^{\circ} , O A = = \sqrt{3}$

To find the coordinates of $A \left(x , y\right)$

${300}^{\circ}$ is in fourth quadrant.

OA forms a triangle with x axis and the three angles are having the measurements of ${30}^{\circ} , {60}^{\circ} , {90}^{\circ}$.

Then the sides will be in the ratio $x : \sqrt{3} x = 2 x$

$x = \overline{O A} \cos \theta = \sqrt{3} \cdot \cos 300 = \sqrt{3} \cos - 60$

$x = \sqrt{3} \cos 60 = \frac{\sqrt{3} \cdot \sqrt{1}}{2} = \frac{\sqrt{3}}{2}$

$y = \overline{O A} \sin \theta = \sqrt{3} \sin 300 = - \sqrt{3} \sin 60$

$y = - \frac{\sqrt{3} \cdot \sqrt{3}}{2} = - \frac{3}{2}$