Question

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

• A. $\frac{5\pi }{6}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (A)

Let $co{t}^{-1}\left(-\sqrt{3}\right)=\theta$
$\Rightarrow cot\theta =-\sqrt{3}$
$=-cot\frac{\pi }{6}$
$=cot\left(\pi -\frac{\pi }{6}\right)$
$=cot\frac{5\pi }{6}$
$\Rightarrow \theta =\frac{5\pi }{6}\in \left(0,\pi \right)$
$\therefore$ Principal value of $co{t}^{-1}\left(-\sqrt{3}\right)$ is $\frac{5\pi }{6}$