Please i need solve these questions

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

1) The right triangle has leg on the positive x-axis and other leg going down ( negative y direction)

the angle at the origin is 30 degrees, so it is 30-60-90 right triangle.

This forces the leg measures to be 1 and sqrt(3), and the hypotenuse to be 2.

The sine of this angle is -sqrt(3)/2.

The other way to see it is to find where the circle and the angle, when promoted to a line, intersect.

The equations are x^2 + y^2 = 1 vs. y = -sqrt(3) * x. THe solution is x=1/2, y =-sqrt(3)/2

2)

cos 2x = 1/2

cos T = 1/2

T = 60 degrees, 300 degrees

x = 30 degrees, 150 degrees

3)

cos(x+x) = cosx*cosx - sinx*sinx = <-- double angle formula as suggested by the hint

cos^2 - sin^2 =

1 - sin^2 - sin^2 = <--- cos^2 = 1 - sin^2

1 - 2*sin^2