Question

Find the principal value $sec^{-1} (2)$

• A. $\frac{\pi}{6}$
• B. $\frac{\pi}{3}$
• C. $\frac{2\pi}{3}$
• D. $\frac{5\pi}{6}$

Answer 1

Answer: (B)

$\frac{\pi}{3}$

Answer 2

Let $sec^{-1} \left(2\right) = \theta$ $\Rightarrow\,sec\,\theta = 2$ $= sec \frac{\pi}{3}$ \Rightarrow\, \theta = \frac{\pi }{3}\in\left[0, \,\pi\right]-\left\\{\frac{\pi}{2}\right\\} $\therefore$ Principal value of $sec^{-1} \left(2\right)$ is $\frac{\pi }{3}$