An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. − 2/sqrt3 cos(3θ) = 1

Question

a) Find all solutions of the equation.

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

Answer 1

cos(3θ) = -√3/2

3θ = 5π/6 + 2kπ or 7π/6 + 2kπ, k = 0, 1, -1, 2, -2, ...

So, θ = 5π/18 + 2kπ/3 or 7π/18 + 2kπ/3

If k = 0, then θ = 5π/18 or 7π/18

If k = 1, then θ = 17π/18 or 19π/18

If k = 2, then θ = 29π/18 or 31π/18

(Other choices for k give solutions that lie outside of the interval [0, 2π))