Answer
$sin~\theta=\frac{\sqrt {21}}{5}$
$tan~\theta=-\frac{\sqrt {21}}{2}$
$cot~\theta=-\frac{2\sqrt {21}}{21}$
$sec~\theta=-\frac{5}{2}$
$csc~\theta=\frac{5\sqrt {21}}{21}$
Work Step by Step
$sin^2\theta+cos^2\theta=1$
$sin^2\theta+(-\frac{2}{5})^2=1$
$sin^2\theta=1-\frac{4}{25}=\frac{21}{25}$
$sin~\theta=\frac{\sqrt {21}}{5}$
$tan~\theta=\frac{sin~\theta}{cos~\theta}=\frac{\frac{\sqrt {21}}{5}}{-\frac{2}{5}}=-\frac{\sqrt {21}}{2}$
$cot~\theta=\frac{cos~\theta}{sin~\theta}=\frac{-\frac{2}{5}}{\frac{\sqrt {21}}{5}}=-\frac{2\sqrt {21}}{21}$
$sec~\theta=\frac{1}{cos~\theta}=-\frac{5}{2}$
$csc~\theta=\frac{1}{sin~\theta}=\frac{5}{\sqrt {21}}=\frac{5\sqrt {21}}{21}$
