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JAMB Mathematics 2013 Paper

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Question : 45

Total: 47

If

\tan \theta = \frac{3}{4}

, find the value of

\sin \theta + \cos \theta

.

$1 \frac{1}{3}$
$1 \frac{2}{3}$
$1 \frac{3}{5}$
$1 \frac{2}{5}$

Solution:

Concept:

Use the right-triangle definitions of sine, cosine, and tangent.

Explanation:

Given

\tan \theta = \frac{3}{4}

, write

\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4}

.

Let opposite

= 3

and adjacent

= 4

.

Find the hypotenuse using Pythagoras:

\text{hypotenuse} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.

Then:

\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{5}, \quad \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{5}.

So:

\sin \theta + \cos \theta = \frac{3}{5} + \frac{4}{5} = \frac{7}{5} = 1 \frac{2}{5}.

Answer:

1 \frac{2}{5}

(Option D).

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