Answer
$\sin{t} = \dfrac{1}{5}$
$\cos{t} =-\dfrac{2\sqrt{6}}{5}$
$\tan{t} =\dfrac{\sqrt{6}}{12}$
$\sec{t} =- \dfrac{5\sqrt{6}}{12}$
$\cot{t} = 2\sqrt{6}$
Work Step by Step
$\because \csc{t} = 5 \hspace{20pt} \therefore \sin{t} = \dfrac{1}{5}$
$\because \cos{t} <0 \\ \therefore \cos{t} = -\sqrt{1-\sin^2{t}} \\ = -\sqrt{1-\left(\dfrac{}1{5}\right)^2} = -\dfrac{2\sqrt{6}}{5}$
$\tan{t} = \dfrac{\sin{t}}{\cos{t}} = \dfrac{\sqrt{6}}{12}$
$\sec{t} = \dfrac{1}{\cos{t}} = - \dfrac{5\sqrt{6}}{12}$
$\cot{t} = \dfrac{1}{\tan{t}} = 2\sqrt{6}$
