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WAEC Mathematics 2018 Paper

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Question : 46

Total: 50

If tan x =

\frac{4}{3}

^{\circ}

^{\circ}

, find the value of sin x - cos x

$\frac{1}{10}$
$\frac{1}{5}$
$\frac{5}{12}$
1 $\frac{2}{5}$

Solution:

Concept:

Use a right-angled triangle to convert

\tan x

into

\sin x

and

\cos x

.

Explanation:

Given

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

and

0^{\circ} < x < 90^{\circ}

, angle

x

is acute.

Let the opposite side be

4

and the adjacent side be

3

.

Using Pythagoras theorem, the hypotenuse

h

is:

h^{2} = 4^{2} + 3^{2} = 16 + 9 = 25

Hence,

h = \sqrt{25} = 5

.

Now,

\sin x = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{4}{5}

.

Also,

\cos x = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3}{5}

.

Therefore,

\sin x - \cos x = \frac{4}{5} - \frac{3}{5} = \frac{1}{5}

.

Answer:

\frac{1}{5}

Correct option: B.

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