Answer
$sin~\theta=\frac{4}{5}$
$cos~\theta=\frac{3}{5}$
$tan~\theta=\frac{4}{3}$
$cot~\theta=\frac{3}{4}$
$sec~\theta=\frac{5}{3}$
$csc~\theta=\frac{5}{4}$
Work Step by Step
Distance from the origin to the given point:
$d=\sqrt {12^2+16^2}=\sqrt {400}=20$
$sin~\theta=\frac{opp}{hyp}=\frac{16}{20}=\frac{4}{5}$
$cos~\theta=\frac{adj}{hyp}=\frac{12}{20}=\frac{3}{5}$
$tan~\theta=\frac{opp}{adj}=\frac{16}{12}=\frac{4}{3}$
$cot~\theta=\frac{adj}{opp}=\frac{12}{16}=\frac{3}{4}$
$sec~\theta=\frac{hyp}{adj}=\frac{20}{12}=\frac{5}{3}$
$csc~\theta=\frac{hyp}{opp}=\frac{20}{16}=\frac{5}{4}$
