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Question
Find the principal solution of the following equation:
Sec θ = `(2)/sqrt(3)`
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Solution
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 1st and 4th quadrant in the interval (0, 2π).
Now in the 1st quadrant,
sec θ = `2/(sqrt3) ⇒ θ = π/6`.
And, in 4th 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`.
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