# If I have a triangle where cos u = -5/7 and sin u >0, how do I find the sine, tangent, cotangent, secant, and cosecant of the angle u?

$\cos u = - \frac{5}{7}$
${\sin}^{2} u = 1 - {\cos}^{2} u = 1 - \frac{25}{49} = \frac{24}{49}$
$\sin u = \frac{2 \sqrt{6}}{7}$
$\tan u = \frac{\sin}{\cos} = \left(\frac{2 \sqrt{6}}{7}\right) \left(- \frac{7}{5}\right) = - \frac{2 \sqrt{6}}{5}$
$\cot u = \frac{1}{\tan} = - \frac{5}{2 \sqrt{6}} = - \frac{5 \sqrt{6}}{12}$
$\sec u = \frac{1}{\cos} = - \frac{7}{5}$
$\csc u = \frac{1}{\sin} = \frac{7}{2 \sqrt{6}} = \frac{7 \sqrt{6}}{12}$