Question

Find the principal solution of the following equation: 

Sec θ = `(2)/sqrt(3)`

Answer 1

We know the principle solution of a trigonometric equation lies in the interval (0, 2π).

For, sec θ = `2/(sqrt3)`,

we know sec θ is positive only in the 1^st and 4^th quadrant in the interval (0, 2π).
Now in the 1^st quadrant,
sec θ = `2/(sqrt3) ⇒ θ = π/6`.

And, in 4^th quadrant,
sec θ = `2/(sqrt3) ⇒ θ = 2π - π/6 = (11π)/6`.

Thus, the principle solution of the equation sec θ = `2/(sqrt3) "is"  θ = π/6 "and" (11π)/6`.