Question

The coordinates of a point on the unit circle subtending an angle of ${30}^{\circ }$ at the origin measured from the positive x-axis in the counter-clockwise direction is:

• A. $(\frac{1}{2},\frac{1}{2})$
  
• B. $(\frac{1}{2},\frac{\sqrt{3}}{2})$
  
• C. $(\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2})$
  
• D. $(\frac{\sqrt{3}}{2},\frac{1}{2})$

Answer 1

The correct option is D $(\frac{\sqrt{3}}{2},\frac{1}{2})$

If $\theta$ is the angle made by segment joining the point circle and origin with the positive x-axis, then the coordinates of the point are given by $(\cos \theta ,\sin \theta )$


Here, $\theta ={30}^{\circ }$
$\therefore$ Co-ordinates of the point $P\equiv \left(\cos \right({30}^{\circ }),\sin ({30}^{\circ }\left)\right)\equiv (\frac{\sqrt{3}}{2},\frac{1}{2})$