What are the coordinates of the terminal point corresponding to = –120? Use the Pythagorean theorem to prove that this point lies on the unit circle?

we know that
the unit circle has a radius equals 1 unit

-120°------> is an angle belong to the III quadrant
so
the x and y coordinates will be negative
x=r*cos ∅
y=r*sin ∅
where
r=1
and 
∅=180-120-----> ∅=60°

therefore
x=(1)*cos 60°-----> x=1/2-----> x=-1/2   (remember x is negative)
y=(1)*sin 60°-----> y=√3/2-----> y=-√3/2  (remember y is negative

let's apply the Pythagorean theorem
x²+y²-----> (-1/2)²+(-√3/2)²----> (1/4)+(3/4)-----> 1----> is ok because 1 is the radius of the unit circle

the answer is
the coordinates of the terminal point are (-1/2,-√3/2)