WAEC Further Mathematics 2015 Paper

Question : 2

Total: 40

Solve:

2\cos x - 1 = 0

Solution:

Concept:

Isolate the trigonometric ratio and identify all angles in the range

[0, 2\pi)

that satisfy the equation.

Explanation:

Start with:

2\cos x - 1 = 0

Add

1

to both sides:

2\cos x = 1

Divide both sides by

2

\cos x = \frac{1}{2}

The principal angle is

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

Since

\cos x

is positive in the first and fourth quadrants, the two solutions in

[0, 2\pi)

are:

x = \frac{\pi}{3}

and

x = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}

Thus, the solution set is

\left\{ \frac{\pi}{3}, \frac{5\pi}{3} \right\}

Answer:

Option D:

\left( \frac{\pi}{3}, \frac{5\pi}{3} \right)

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