Question

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 cos(2θ) − 1 = 0 Find the solutions in the interval [0, 2π).

Answer 1

Se below in bold.

Explanation:

2 cos(2θ) − 1 = 0

cos(2θ) = 0.5

2(cosθ)^2 - 1 = 0.5

2(cosθ)^2 = 1.5

(cosθ)^2 = 0.75

cosθ = +/- √0.75 = +/-0.866

So, θ = π/6, 5π/6, 7π/6, 11π/6 (in the interval {0, 2π).