Answer
$\sin\theta=-\frac{2\sqrt 5}{5}$
$\sec\theta=\sqrt 5$
$\csc\theta=-\frac{\sqrt 5}{2}$
$\tan\theta=-2$
$\cot\theta=-\frac{1}{2}$
Work Step by Step
$\sin^{2}\theta+\cos^{2}\theta=1\implies\sin^{2}\theta=1-\cos^{2}\theta$
$=1-(\frac{1}{\sqrt 5})^{2}=\frac{4}{5}$
$\sin\theta$ is negative in the fourth quadrant. Therefore,
$\sin\theta=-\sqrt {\frac{4}{5}}=-\frac{2}{\sqrt 5}=-\frac{2\sqrt 5}{5}$
$\sec\theta=\frac{1}{\cos\theta}=\sqrt 5$
$\csc\theta=\frac{1}{\sin\theta}=-\frac{\sqrt 5}{2}$
$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{-\frac{2}{\sqrt 5}}{\frac{1}{\sqrt 5}}=-2$
$\cot\theta=\frac{1}{\tan\theta}=-\frac{1}{2}$
