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WAEC Further Mathematics 2013 Paper

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Question : 2

Total: 40

Solve:

\sin\;\theta = \tan\theta

200°
90°
60°
0°

Solution:

Concept:

Solve the trigonometric equation by writing

\tan\theta

as

\frac{\sin\theta}{\cos\theta}

and then factoring.

Explanation:

Given:

\sin\theta = \tan\theta

.

Since

\tan\theta = \frac{\sin\theta}{\cos\theta}

, we get

\sin\theta = \frac{\sin\theta}{\cos\theta}

.

Multiply both sides by

\cos\theta

:

\sin\theta\cos\theta = \sin\theta

.

Bring all terms to one side:

\sin\theta\cos\theta - \sin\theta = 0

.

Factor out

\sin\theta

:

\sin\theta(\cos\theta - 1) = 0

.

Thus, either

\sin\theta = 0

or

\cos\theta = 1

.

From the options,

\theta = 0^{\circ}

satisfies both conditions.

Answer:

D.

0^{\circ}

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