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WAEC Mathematics 2019 Paper

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Question : 36

Total: 50

If tan x =

\;\frac{3}{4}

^{\circ}

\;\frac{\cos\;x}{2\;\sin\;x}

$\;\frac{8}{3}$
$\;\frac{3}{2}$
$\;\frac{4}{3}$
$\;\frac{2}{3}$

Solution:

Concept:

Use the right-triangle definition of

\tan x

to find

\sin x

and

\cos x

, then substitute into the given expression.

Explanation:

Given

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

and

0 < x < 90^{\circ}

, the triangle has opposite side

3

and adjacent side

4

.

Find the hypotenuse

y

using Pythagoras theorem:

y^2 = 3^2 + 4^2 = 9 + 16 = 25

So

y = 5

.

Therefore,

\sin x = \frac{3}{5}

and

\cos x = \frac{4}{5}

.

Now evaluate the expression:

\frac{\cos x}{2\sin x} = \frac{\frac{4}{5}}{2 \times \frac{3}{5}}

= \frac{\frac{4}{5}}{\frac{6}{5}}

= \frac{4}{5} \times \frac{5}{6}

= \frac{4}{6} = \frac{2}{3}

Answer:

\frac{2}{3}

, which is Option D.

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