WAEC 2021 · Paper 1 · Q22

If $\tan\theta = \frac34$ and $180^\circ < \theta < 270^\circ$ , find the value of $\cos\theta$ .

Worked solution (try it first)

$\tan\theta = \frac34$ gives a reference triangle with opposite 3, adjacent 4 and hypotenuse $\sqrt{9 + 16} = 5$ , so the size of $\cos\theta$ is $\frac45$ .
$180^\circ < \theta < 270^\circ$ is the third quadrant, where cosine is negative.
So $\cos\theta = -\frac45$ , option C.