Answer
$cos~\theta=\frac{adj}{hyp}=\frac{4\sqrt 5}{9}$
$sin~\theta=\frac{opp}{hyp}=\frac{1}{9}$
$tan~\theta=\frac{opp}{adj}=\frac{1}{4\sqrt 5}=\frac{\sqrt 5}{20}$
$cot~\theta=\frac{adj}{opp}=\frac{4\sqrt 5}{1}=4\sqrt 5$
$sec~\theta=\frac{hyp}{adj}=\frac{9}{4\sqrt 5}=\frac{9\sqrt 5}{20}$
Work Step by Step
$csc~\theta=\frac{hyp}{opp}$
$9=\frac{hyp}{opp}$
Use the pythagorean theorem to find the adjacent side of $\theta$
$9^2=1^2+adj^2$
$adj^2=81-1=80$
$adj=4\sqrt 5$
$cos~\theta=\frac{adj}{hyp}=\frac{4\sqrt 5}{9}$
$sin~\theta=\frac{opp}{hyp}=\frac{1}{9}$
$tan~\theta=\frac{opp}{adj}=\frac{1}{4\sqrt 5}=\frac{\sqrt 5}{20}$
$cot~\theta=\frac{adj}{opp}=\frac{4\sqrt 5}{1}=4\sqrt 5$
$sec~\theta=\frac{hyp}{adj}=\frac{9}{4\sqrt 5}=\frac{9\sqrt 5}{20}$