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WAEC Mathematics 2012 Paper

Question : 17

Total: 49

If cos(x + 40)^o = 0.0872, what is the value of x?

Solution:

Concept:

Use the inverse cosine function to find the angle whose cosine is

0.0872

, then solve algebraically for

x

Explanation:

Start with the given equation:

\cos(x + 40)^\circ = 0.0872

Apply

\cos^{-1}

to both sides to remove the cosine:

(x + 40)^\circ = \cos^{-1}(0.0872)

From trigonometric tables or a calculator,

\cos^{-1}(0.0872) = 85^\circ

because

\cos 85^\circ = 0.0872

So,

x + 40 = 85

Subtract

40

from both sides:

x = 85 - 40

x = 45^\circ

Answer:

x = 45^\circ

, which is option D.

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