Question

What is the principle value of \(sec^{-1}⁡(\frac{2}{\sqrt{3}})\).

(a) \(\frac{π}{6}\)

(b) \(\frac{π}{3}\)

(c) \(\frac{π}{4}\)

(d) \(\frac{π}{2}\)

I have been asked this question during an interview for a job.

My question is based upon Inverse Trigonometric Functions Basics in section Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Right option is (a) \(\frac{π}{6}\)

To elaborate: Let \(sec^{-1}⁡(\frac{2}{\sqrt{3}})\)=y

sec⁡ y=\(\frac{2}{\sqrt{3}}\)

sec⁡ y=sec \(⁡\frac{π}{6}\)

⇒y=\(\frac{π}{6}\)