Answer
$\sin{t} =\dfrac{12}{13}$
$\cos{t} =-\dfrac{5}{13}$
$\csc{t} =\dfrac{13}{12}$
$\sec{t} = -\dfrac{13}{5}$
$\cot{t} =-\dfrac{5}{12}$
Work Step by Step
$\tan{t} =-\dfrac{12}{5}$
$\because \sin{t}>0 \hspace{5pt} \& \tan{t} < 0 \hspace{20pt} \therefore \cos{t} $ is negative
$\sec^2{t} = 1+\tan^2{t} \\ \sec{t} = -\sqrt{1+\tan^2{t}} \\ = -\sqrt{1+\left(\dfrac{-12}{5}\right)^2} = -\dfrac{13}{5}$
$\cos{t} = \dfrac{1}{\sec{t}} = -\dfrac{5}{13}$
$\sin{t} = \cos{t} \times \tan{t} =\dfrac{12}{13}$
$\csc{t} = \dfrac{1}{\sin{t}} = \dfrac{13}{12}$
$\cot{t} = \dfrac{1}{\tan{t}} =-\dfrac{5}{12}$
