An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. − 2 cos 3θ = 1

Question

(a) Find all solutions of the equation

(b) Find the solutions in the interval [0, 2π).

Answer 1

cos(3θ) = -1/2

3θ = 2π/3 + 2kπ or 4π/3 + 2kπ

So, θ = 2π/9 + 2kπ/3 or 4π/9 + 2kπ/3

If k = 0, then θ = 2π/9, 4π/9

If k = 1, then θ = 8π/9, 10π/9

If k = 2, then θ = 14π/9, 16π/9

Other values of k give values of θ that lie outside of the interval [0, 2π).