Find all solutions to the equation.

Question

 cos (x) = 1/-2?  

Answer 1

The trigonometric equation is cos(x) = - 1/2.

The cosine function is negative in second and third quadrant.

In second quadrant (π/2 < θ < π),

- 1/2 = - cos(π/3) = cos(π - π/3) = cos(2π/3).

General solution : If cos(θ) = cos(α), then θ = 2nπ ± α, where n is an integer.

If α = 2π/3, then x = 2nπ ± 2π/3.

The general solution x = 2nπ ± 2π/3 , where n is an integer.