Question

Find the principal value $cos^{-1} \left(\frac{-\sqrt{3}}{2}\right)$

• A. $\frac{5\pi}{6}$
• B. $\frac{\pi}{6}$
• C. $\frac{4\pi}{9}$
• D. $\frac{2\pi}{3}$

Answer 1

Answer: (A)

Let $cos^{-1} \left(\frac{-\sqrt{3}}{2}\right) = \theta$
$\Rightarrow \,cos\,\theta = \frac{-\sqrt{3}}{2}$
$= -cos \frac{\pi }{6}$
$= cos\left(\pi - \frac{\pi}{6}\right)$
$= cos \frac{5\pi}{6}$
$\Rightarrow \,\theta = \frac{5\pi }{6}\in \left[0,\,\pi\right]$
$\therefore $ Principal value of $cos^{-1} \left(\frac{-\sqrt{3}}{2}\right)$ is $\frac{5\pi}{6}$