Question

Evaluate:
$\cos \left(\frac{\pi }{2}-{\sin }^{-1}\left(-\frac{1}{2}\right)\right\}.$

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. $-\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $-\frac{1}{2}$

$\cos \left(\frac{\pi }{2}-{\sin }^{-1}\left(-\frac{1}{2}\right)\right\}$
$=\cos \left(\frac{\pi }{2}-\left(-\frac{\pi }{6}\right)\right)$
$=\cos \frac{2\pi }{3}$
$=-\frac{1}{2}$