# How do you find the value of cotθ if cosθ = -4/5?

${\sin}^{2} x = 1 - {\cos}^{2} x = 1 - \frac{16}{25} = \frac{9}{25} \to \sin x = \pm \frac{3}{5}$
$\cos x = - \frac{4}{5}$, then x is in Quadrant II, sin x is positive$\left(\frac{3}{5}\right)$
$\cot x = \cos \frac{x}{\sin} x = \left(- \frac{4}{5}\right) : \left(\frac{3}{5}\right) = - \frac{4}{3}$