If the terminal side of a 330 degree angle intersects a unit circle, what would the coordinates at the point of intersection?

Question

1. If the terminal side of a 330 degree angle intersects a unit circle, what would the coordinates at the point of intersection?

2. Solve for x: 3 + cos 2x = 7/2; only include answers on [0, 2π]

3. Verify the following identity by using an angle sum identity: cos (2x) = 1 – 2(sin² x). Hint (2x = x + x)

Answer 1

An angle of 330° is coterminal with an angle of -30° in the fourth quadrant. Since it forms a right triangle with a hypotenuse of 1 (since it is on the unit circle), the x-coordinate is equal to the cosine of -30° and the y-coordinate is equal to the sine of -30°.

 

So the coordinates are  (√3/2, -1/2)