Answer
$sin~\theta=\frac{3\sqrt {10}}{10}$
$cos~\theta=-\frac{\sqrt {10}}{10}$
$tan~\theta=-3$
$cot~\theta=-\frac{1}{3}$
$sec~\theta=-\sqrt {10}$
$csc~\theta=\frac{\sqrt {10}}{3}$
Work Step by Step
Distance from the origin to the given point:
$d=\sqrt {(-2)^2+6^2}=\sqrt {40}=2\sqrt {10}$
$sin~\theta=\frac{opp}{hyp}=\frac{6}{2\sqrt {10}}=\frac{3\sqrt {10}}{10}$
$cos~\theta=\frac{adj}{hyp}=\frac{-2}{2\sqrt {10}}=-\frac{\sqrt {10}}{10}$
$tan~\theta=\frac{opp}{adj}=\frac{6}{-2}=-3$
$cot~\theta=\frac{adj}{opp}=\frac{-2}{6}=-\frac{1}{3}$
$sec~\theta=\frac{hyp}{adj}=\frac{2\sqrt {10}}{-2}=-\sqrt {10}$
$csc~\theta=\frac{hyp}{opp}=\frac{2\sqrt {10}}{6}=\frac{\sqrt {10}}{3}$
