Answer
$ \sin{t} = \dfrac{2\sqrt{6}}{5}$
$ \cos{t} = -\dfrac{1}{5}$
$\tan{t} =-2 \sqrt{6}$
$\csc{t} =\dfrac{5 \sqrt{6}}{12}$
$\sec{t} =-5$
$\cot{t} = -\dfrac{\sqrt{6}}{12}$
Work Step by Step
With $P= \left(-\dfrac{1}{5},\dfrac{2\sqrt{6}}{5} \right) = (x,y)$, then $x = -\dfrac{1}{5} \text{ and } \hspace{15pt} y =\dfrac{2\sqrt{6}}{5}$.
Thus,
$\sin{t} = y$
$ \sin{t} = \dfrac{2\sqrt{6}}{5}$
$\cos{t} = x$
$ \cos{t} = -\dfrac{1}{5}$
$\tan{t} = \dfrac{y}{x}$
$\tan{t} = \dfrac{\dfrac{2\sqrt{6}}{5}}{ -\dfrac{1}{5} } = -2 \sqrt{6}$
$\csc{t} = \dfrac{1}{y}$
$\csc{t} = \dfrac{1}{\dfrac{2\sqrt{6}}{5}} = \dfrac{5 \sqrt{6}}{12}$
$\sec{t} = \dfrac{1}{x}$
$\sec{t} = \dfrac{1}{-\dfrac{1}{5}}= -5$
$\cot{t} = \dfrac{x}{y}$
$\cot{t} = \dfrac{-\dfrac{1}{5} }{\dfrac{2\sqrt{6}}{5}} = -\dfrac{\sqrt{6}}{12}$