Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)

A.

\(\frac{-2}{\sqrt{3}}\)

B.

\(\frac{-\sqrt{3}}{2}\)

C.

\(\frac{\sqrt{3}}{4}\)

D.

\(\frac{4}{\sqrt{3}}\)

Correct answer is B

\(\cos (x + y) = \cos x \cos y - \sin x \sin y\)

\(\cos (\frac{\pi}{2} + \frac{\pi}{3}) = \cos \frac{\pi}{2} \cos \frac{\pi}{3} - \sin \frac{\pi}{2} \sin \frac{\pi}{3}\)

= \((0 \times \frac{1}{2}) - (1 \times \frac{\sqrt{3}}{2})\)

= \(0 - \frac{\sqrt{3}}{2} = -\frac{\sqrt{3}}{2}\)