# What are the coordinates for the point p((11pi)/3) where p(theta)=(x,y) is the point where the terminal arm of an angle theta intersects the unit circl?

Mar 19, 2018

$P \left(\frac{1}{2} , - \frac{\sqrt{3}}{2}\right)$

#### Explanation:

By the definitions of trig functions, the point P has as coordinates: -
P(x, y)
$x = \cos \left(\frac{11 \pi}{3}\right)$, and $y = \sin \left(\frac{11 \pi}{3}\right)$
Trig table and unit circle give -->
$x = \cos \left(\frac{11 \pi}{3}\right) = \cos \left(- \frac{\pi}{3} + 4 \pi\right) = \cos \left(- \frac{\pi}{3}\right) = \cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$
$y = \sin \left(\frac{11 \pi}{3}\right) = \sin \left(- \frac{\pi}{3} + 4 \pi\right) = \sin \left(- \frac{\pi}{3}\right) =$
$- \sin \left(\frac{\pi}{3}\right) = - \frac{\sqrt{3}}{2}$
Answer: $P \left(\frac{1}{2} , - \frac{\sqrt{3}}{2}\right)$.
Note. P is in Quadrant 4.