MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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)

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)