Answer
$cos~\theta=\frac{adj}{hyp}=\frac{2\sqrt 6}{5}$
$tan~\theta=\frac{opp}{adj}=\frac{\sqrt 6}{12}$
$cot~\theta=\frac{adj}{opp}=2\sqrt 6$
$sec~\theta=\frac{hyp}{adj}=\frac{5\sqrt 6}{12}$
$csc~\theta=\frac{hyp}{opp}=5$
Work Step by Step
$sin~\theta=\frac{opp}{hyp}$
$\frac{1}{5}=\frac{opp}{hyp}$
Use the pythagorean theorem to find the adjacent side of $\theta$
$5^2=1^2+adj^2$
$adj^2=25-1=24$
$adj=2\sqrt 6$
$cos~\theta=\frac{adj}{hyp}=\frac{2\sqrt 6}{5}$
$tan~\theta=\frac{opp}{adj}=\frac{1}{2\sqrt 6}=\frac{\sqrt 6}{12}$
$cot~\theta=\frac{adj}{opp}=\frac{2\sqrt 6}{1}=2\sqrt 6$
$sec~\theta=\frac{hyp}{adj}=\frac{5}{2\sqrt 6}=\frac{5\sqrt 6}{12}$
$csc~\theta=\frac{hyp}{opp}=\frac{5}{1}=5$
