Homework: Double Angle Identities (Section 7.3)

Question

Solve  for all solutions 

Give your answers accurate as a list separated by commas

Answer 1

c2-(c)^2 =-3/8 (c=cos2)

2c^2-1 -c^2 = -3/8

c^2 = 5/8

c = +sqr(5/8) = +0.79

w = 37.76 or 322.24, or 142.24 or 217.76 degrees

4 different angles between 0 and 360

Answer 2

8cos(2w) = 8cos²w - 3;

8(2cos²w - 1) - 8cos²w + 3 = 0;

8cos²w - 5 = 0; 4cos(2w) - 1 = 0

cos(2w) = 1/4; 2w = cos^-1(1/4) + 2πn; x = 1/2cos^-1(1/4) + πn

or (2x) = 2π - cos^-1(1/4) + 2πn; x = π - 1/2cos^-1(1/4) + πn;

Verying n = 0, 1,2,.. we will get all solutions: n = 0: x = 1/2cos^-1(1/4); x = π - 1/2cos^-1(1/4)

n = 1: x = 1/2cos^-1(1/4) + π, x = 2π - 1/2cos^-1(1/4).

For n = 2, 3,.. we will get zeros outside of interval [0, 2π)

Answer 3

Would you know if my answer was inaccurate?

8 cos 2w = 8 cos² w - 3

8 cos 2w - 8 cos² w = -3

cos 2w - cos² w = -3 / 8

2 cos² w - 1 - cos² w = -3 / 8

cos² w - 1 = -3 / 8

cos² w = 5 / 8

Can you complete and answer?