If sin x = 5/13 and 0 o ≤ x ≤ 90 o , find the value of (cos x - tan x)

Correct Answer is : 7915679/15615679

Correct Answer is : 7915679/15615679

Test Index

WAEC Mathematics 2013 Paper

Question : 16

Total: 48

If sin x =

\frac{5}{13}

\leq

\leq

90^o, find the value of (cos x - tan x)

Solution:

Concept:

Use right-triangle trigonometry to find

\cos x

and

\tan x

from the given

\sin x

Explanation:

Given

\sin x = \frac{5}{13}

with

0^\circ \leq x \leq 90^\circ

, take the opposite side as

5

and the hypotenuse as

13

Find the adjacent side using Pythagoras:

13^2 = 5^2 + \text{adjacent}^2

\text{adjacent}^2 = 169 - 25 = 144

, giving adjacent side

= 12

Thus

\cos x = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13}

And

\tan x = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{12}

Now compute:

\cos x - \tan x = \frac{12}{13} - \frac{5}{12}

This equals

\frac{144 - 65}{156} = \frac{79}{156}

Answer:

\frac{79}{156}

, which is option C.

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