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Math·Geometry and Trigonometry·Right triangles and trigonometry

hard

Point $N$ lies on a unit circle in the $xy$-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 $NOM$ is $\frac{272\pi }{3}$ radians. If the coordinates of point $M$ are $(a,b)$, where $a$ and $b$ are constants, what is the value of $a$?

A

$\frac{1}{2}$

B

$\frac{\sqrt{3}}{2}$

C

$-\frac{1}{2}$

D

$-\frac{\sqrt{3}}{2}$