Question

The principle solutions of the equation cos θ = `1/2` are ______.

Options

• `π/6, (5π)/6`

• `π/3, (5π)/3`

• `π/6, (7π)/6`

• `π/3, (2π)/3`

Answer 1

The principle solutions of the equation cos θ = `1/2` are `bbunderline(π/3, (5π)/3)`.

Explanation:

cos θ = `1/2`

= cos `π/3`

= `cos (2π - π/3)`

= `cos  (5 pi)/3`

∴ Principal solution: `pi/3, (5 pi)/3` ∈ (0. 2π)

∴ `π/3, (5π)/3`