Point $N$ lies on a unit circle in the $xy$-plane and has coordinates…

Question

Prompt

Point

N

lies on a unit circle in the

x y

-plane and has coordinates

(1, 0)

. Point

O

is the center of the circle and has coordinates

(0, 0)

. Point

M

also lies on the unit circle, and the measure of angle

N O M

\frac{272 π}{3}

radians. If the coordinates of point

M

are

(a, b)

, where

a

and

b

are constants, what is the value of

a

1/2

3 /2

- 1/2

- 3 /2