WAEC 2023 · Paper 2 · Q4

(a)
The gradient of the line joining the points $(-2, n)$ and $(n, 5)$ is $\frac43$ . Find the value of $n$ .
(b)
Given that $\tan x = \frac{15}{8}$ , $0^\circ < x < 90^\circ$ , find the value of $5\sin x - 6\cos x$ .

Worked solution (try it first)

$\tan x = \frac{15}{8}$ : the hypotenuse is $\sqrt{15^2 + 8^2} = 17$ , so $\sin x = \frac{15}{17}$ and $\cos x = \frac{8}{17}$ .
Then $5\sin x - 6\cos x = \frac{75}{17} - \frac{48}{17}$
$= \frac{27}{17}$ .