Question

Find the principal value $tan^{-1} \, \left(\sqrt{3}\right)$

• 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 $tan^{-1} \left(\sqrt{3}\right) = \theta$ $\Rightarrow tan\,\theta = \sqrt{3}$ $= tan \frac{\pi}{3}$ $\Rightarrow \theta = \frac{\pi }{3} \in \left(\frac{-\pi }{2}, \frac{\pi}{2}\right)$ $\therefore$ Principal value of $tan^{-1} \left(\sqrt{3}\right)$ is $\frac{\pi}{3}$