# Given cos x = -3/4 and sin x is negative, what are the values of the remaining trigonometric functions?

May 21, 2016

Use the trig identity: ${\sin}^{2} x + {\cos}^{2} x = 1$
$\cos x = - \frac{3}{4}$ --> ${\sin}^{2} x = 1 - \left(\frac{9}{16}\right) = \frac{7}{16}$ ---> $\sin x = - \frac{\sqrt{7}}{4}$
$\tan x = \sin \frac{x}{\cos x} = - \frac{\sqrt{7}}{3}$
$\cot x = - \frac{3}{\sqrt{7}} = - \frac{3 \sqrt{7}}{7}$
$\sec x = \frac{1}{\cos x} = - \frac{4}{3}$
$\csc x = \frac{1}{\sin x} = - \frac{4}{\sqrt{7}} = - \frac{4 \sqrt{7}}{7}$