Question

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

• A. $3\pi /4$
• B. $\pi /4$
• C. $\pi$
• D. none of these

Answer 1

The correct option is A $3\pi /4$

Principle value of ${\cos }^{-1}\left(\frac{-1}{\sqrt{2}}\right)$

$={\cos }^{-1}(-\cos \frac{\pi }{4})$

$={\cos }^{-1}\left(\cos \right(\pi -\frac{\pi }{4}\left)\right)$

$=\pi -\frac{\pi }{4}$

$=\frac{3\pi }{4}$