Answer
$ \tan{\theta}=\dfrac{1}{2}$
$ \csc{\theta} =-\sqrt{5}$
$\sec{\theta} =-\dfrac{\sqrt{5}}{2}$
$\cot{\theta} =2$
Work Step by Step
$\tan{\theta}= \dfrac{\sin{\theta}}{\cos{\theta}}$
$\therefore \tan{\theta}= \dfrac{-\dfrac{\sqrt{5}}{5}}{-\dfrac{2\sqrt{5}}{5}}=\dfrac{1}{2}$
$\csc{\theta} = \dfrac{1}{\sin{\theta}}$
$\therefore \csc{\theta} = \dfrac{1}{-\dfrac{\sqrt{5}}{5}}=-\sqrt{5}$
$\sec{\theta} = \dfrac{1}{\cos{\theta}}$
$\therefore \sec{\theta} = \dfrac{1}{-\dfrac{2\sqrt{5}}{5}}= -\dfrac{\sqrt{5}}{2}$
$\cot{\theta} = \dfrac{1}{\tan{\theta}}$
$\cot{\theta} = \dfrac{1}{\dfrac{1}{2}}= 2$
