Answer
$\cos{t} =-\dfrac{\sqrt{15}}{4}$
$\tan{t}= \dfrac{\sqrt{15}}{15}$
$\csc{t} =-4$
$\sec{t} =\dfrac{4\sqrt{15}}{15}$
$\cot{t} =\sqrt{15}$
Work Step by Step
$\because \sec{t} <0 \hspace{20pt} \therefore \cos{t} <0$
$\cos{t} = - \sqrt{1-\sin^2{t}} \\ = - \sqrt{1-\left(\dfrac{-1}{5}\right) ^2} = -\dfrac{\sqrt{15}}{4}$
$\tan{t}= \dfrac{\sin{t}}{\cos{t}} = \dfrac{\sqrt{15}}{15}$
$\csc{t} = \dfrac{1}{\sin{t}} = -4$
$\sec{t} = \dfrac{1}{\cos{t}} = \dfrac{4\sqrt{15}}{15}$
$\cot{t} = \dfrac{1}{\tan{t}} = \sqrt{15}$
