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Find the principal solution of the following equation: Sec θ = 23 - Mathematics and Statistics

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Question

Find the principal solution of the following equation: 

Sec θ = `(2)/sqrt(3)`

Sum
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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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Chapter 3: Trigonometric Functions - Exercise 3.1 [Page 75]

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