# How do you find the exact values of the remaining five trigonometric functions of angle, given csc of the angle is -4?

$\csc x = \frac{1}{\sin} x = - 4 \to \sin x = - \frac{1}{4}$
${\cos}^{2} x = 1 - {\sin}^{2} x = 1 - \frac{1}{16} = \frac{15}{16} \to \cos x = \pm \frac{\sqrt{15}}{4}$
$\tan x = - \left(\frac{1}{4}\right) \left(\frac{4}{\sqrt{15}}\right) = \frac{- s q r 15}{15}$
$\cot x = - \frac{15}{\sqrt{15}} = \frac{- 15 \sqrt{15}}{15} = - \sqrt{15}$
$\sec x = \frac{1}{\cos} x = - \frac{4}{\sqrt{15}}$ = $- \frac{4 \sqrt{15}}{15}$