WAEC 2021 · Paper 1 · Q38

Trigonometric ratios

Given that $\sin x = \frac35$ , $0^\circ \le x \le 90^\circ$ , evaluate $(\tan x + 2\cos x)$ .

Worked solution (try it first)

$\sin x = \frac35$ gives a triangle with opposite 3 and hypotenuse 5.
Pythagoras gives the adjacent side $\sqrt{25 - 9} = 4$ .
So $\cos x = \frac45$ and $\tan x = \frac34$ .
Then $\tan x + 2\cos x = \frac34 + \frac85$ .
Over 20 this is $\frac{15}{20} + \frac{32}{20} = \frac{47}{20}$ .
As a mixed number, $\frac{47}{20} = 2\frac{7}{20}$ , option C.

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