Question

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?

Answer 1

`P(1/2, - sqrt3/2)`

Explanation:

By the definitions of trig functions, the point P has as coordinates: -
P(x, y)
`x = cos ((11pi)/3)`, and `y = sin ((11pi)/3)`
Trig table and unit circle give -->
`x = cos ((11pi)/3) = cos (-pi/3 + 4pi) = cos (-pi/3) = cos (pi/3) = 1/2`
`y = sin ((11pi)/3) = sin (-pi/3 + 4pi) = sin (- pi/3) =`
`- sin (pi/3) = -sqrt3/2`
Answer: `P(1/2, -sqrt3/2)`.
Note. P is in Quadrant 4.