Evaluate ≤ft(π/2 + π/3)

Correct Answer is : −32{-{3}}{2}2−3

Correct Answer is : −32{-{3}}{2}2−3

Test Index

WAEC Further Mathematics 2011 Paper

Question : 4

Total: 40

Evaluate

\cos\left(\frac{\pi}{2} + \frac{\pi}{3}\right)

Solution:

Concept:

Use the cosine addition formula:

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

Explanation:

Here,

x = \frac{\pi}{2}

and

y = \frac{\pi}{3}

Substitute into the formula:

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

Now use standard values:

\cos\frac{\pi}{2} = 0

\cos\frac{\pi}{3} = \frac{1}{2}

\sin\frac{\pi}{2} = 1

\sin\frac{\pi}{3} = \frac{\sqrt{3}}{2}

So the expression becomes:

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

Answer:

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

, which is option B.

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