Give the smallest two solutions of cos (2θ) = 0.8212 on [0, 2π). Separate the two solutions with a comma

Question

Give the smallest two solutions of cos (2θ) = 0.8212 on [0, 2π). Separate the two solutions with a comma

Answer 1

Let x = 2 theta

so cos x =.8212 take inverse cos of both sides to solve for x\

x= =34.7949 degrees Theta is 1/2 x so theta =17.397 or 17.40 rounded to nearest hundreth

cosine is also positive in quadrant 4 so the other angle is (360- 34.7949)/2. or 162.75 degrees

Answer 2

cos 2θ = 0.8212

2θ ≈ 0.6073^r