Answer
$\sin{t} = \dfrac{4\sqrt{17}}{17}$
$\cos{t} = -\dfrac{\sqrt{17}}{17}$
$\csc{t} =\dfrac{\sqrt{17}}{4}$
$\sec{t}=-\sqrt{17}$
$\cot{t} =-\dfrac{1}{4}$
Work Step by Step
$\tan{t} =-4$
$\because \csc{t} > 0 \hspace{5pt} \& \tan{t} < 0 \hspace{20pt} \therefore \sec{t} $ is negative
$\sec^2{t} = 1+\tan^2{t} \\ \sec{t} = -\sqrt{1+\tan^2{t}} \\ = -\sqrt{1+(-4)^2} = \sec{t} =-\sqrt{17}$
$\cos{t} = \dfrac{1}{\sec{t}} = -\dfrac{\sqrt{17}}{17}$
$\sin{t} = \cos{t} \times \tan{t} = \dfrac{4\sqrt{17}}{17}$
$\csc{t} = \dfrac{1}{\sin{t}} = \dfrac{\sqrt{17}}{4}$
$\cot{t} = \dfrac{1}{\tan{t}} =-\dfrac{1}{4}$