# How do you determine all trigonometric ratios given cotθ=11/7?

Nov 7, 2015

Find 6 trig functions knowing $\cot x = \frac{11}{7}$
$\cot x = \frac{11}{7}$ --> $\tan x = \frac{7}{11.}$
hypotenuse: ${h}^{2} = {7}^{2} + {11}^{2} = 49 + 121 = 170$ --> $h = 13.04 .$
$\sin x = \frac{7}{h} = \frac{7}{13.04} = 0.54$
$\cos x = \frac{11}{h} = \frac{11}{13.04} = 0.84$
$\sec x = \frac{1}{\cos} = 1.86$
$\csc x = \frac{1}{\sin} = 1.19$