Answer
$sin~θ=\frac{3}{5}$
$cos~θ=\frac{4}{5}$
$tan~θ=\frac{3}{4}$
$csc~θ=\frac{5}{3}$
$sec~θ=\frac{5}{4}$
$cot~θ=\frac{4}{3}$
Work Step by Step
First, let's evaluate the hypotenuse:
$(hyp)^2=(opp)^2+(adj)^2$
$hyp=\sqrt {8^2+6^2}=\sqrt {100}=10$
$sin~θ=\frac{opp}{hyp}=\frac{6}{10}=\frac{3}{5}$
$cos~θ=\frac{adj}{hyp}=\frac{8}{10}=\frac{4}{5}$
$tan~θ=\frac{opp}{adj}=\frac{6}{8}=\frac{3}{4}$
$csc~θ=\frac{hyp}{opp}=\frac{10}{6}=\frac{5}{3}$
$sec~θ=\frac{hyp}{adj}=\frac{10}{8}=\frac{5}{4}$
$cot~θ=\frac{adj}{opp}=\frac{8}{6}=\frac{4}{3}$
