Question

Find the solution of cos θ = `1/2`, where 0 ≤ θ < 2π.

Answer 1

We know that, `cos  pi/3 = 1/2` and cos (2π − θ) = cos θ

∴ `cos  pi/3 = cos(2pi - pi/3) = cos  (5pi)/3`

∴ `cos  pi/3 = cos  (5pi)/3 = 1/2`, where

`0 < pi/3 < 2pi and 0 < (5pi)/3 < 2pi`

∴ `cos θ = 1/2` gives cos θ `= cos  pi/3 = cos  (5pi)/3`

∴ `θ = pi/3` and `θ = (5pi)/3`

Hence, the required solutions are `θ = pi/3` and `θ = (5pi)/3`.