Answer
$cos~\theta=\frac{adj}{hyp}=\frac{4}{5}$
$tan~\theta=\frac{opp}{adj}=\frac{3}{4}$
$cot~\theta=\frac{adj}{opp}=\frac{4}{3}$
$sec~\theta=\frac{hyp}{adj}=\frac{5}{4}$
$csc~\theta=\frac{hyp}{opp}=\frac{5}{3}$
Work Step by Step
$sin~\theta=\frac{opp}{hyp}$
$\frac{3}{5}=\frac{opp}{hyp}$
Use the pythagorean theorem to find the adjacent side of $\theta$
$5^2=3^2+adj^2$
$adj^2=25-9=16$
$adj=4$
$cos~\theta=\frac{adj}{hyp}=\frac{4}{5}$
$tan~\theta=\frac{opp}{adj}=\frac{3}{4}$
$cot~\theta=\frac{adj}{opp}=\frac{4}{3}$
$sec~\theta=\frac{hyp}{adj}=\frac{5}{4}$
$csc~\theta=\frac{hyp}{opp}=\frac{5}{3}$
