Answer
$cos~\theta=\frac{1}{2}$
$sin~\theta=\frac{\sqrt 3}{2}$
$tan~\theta=\sqrt 3$
$cot~\theta=\frac{\sqrt 3}{3}$
$sec~\theta=2$
$csc~\theta=\frac{2\sqrt 3}{3}$
Work Step by Step
$hyp=8$
$adj=4$
Use the pythagorean theorem to find the opposite side of $\theta$
$8^2=4^2+opp^2$
$opp^2=64-16=48$
$opp=4\sqrt 3$
$cos~\theta=\frac{adj}{hyp}=\frac{4}{8}=\frac{1}{2}$
$sin~\theta=\frac{opp}{hyp}=\frac{4\sqrt 3}{8}=\frac{\sqrt 3}{2}$
$tan~\theta=\frac{opp}{adj}=\frac{4\sqrt 3}{4}=\sqrt 3$
$cot~\theta=\frac{adj}{opp}=\frac{4}{4\sqrt 3}=\frac{\sqrt 3}{3}$
$sec~\theta=\frac{hyp}{adj}=\frac{8}{4}=2$
$csc~\theta=\frac{hyp}{opp}=\frac{8}{4\sqrt 3}=\frac{2\sqrt 3}{3}$
