Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)
FURTHER MATHEMATICS
WAEC 2011
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: B. \(\frac{-\sqrt{3}}{2}\)
Explanation
\(\cos (x + y) = \cos x \cos y - \sin x \sin y\)
\(\cos (\frac{\pi}{2} + \frac{\pi}{3}) = \cos \frac{\pi}{2} \cos \frac{\pi}{3} - \sin \frac{\pi}{2} \sin \frac{\pi}{3}\)
= \((0 \times \frac{1}{2}) - (1 \times \frac{\sqrt{3}}{2})\)
= \(0 - \frac{\sqrt{3}}{2} = -\frac{\sqrt{3}}{2}\)
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