Answer
$ \sin{t} = \dfrac{\sqrt{21}}{5}$
$ \cos{t} = -\dfrac{2}{5}$
$\tan{t} =-\dfrac{\sqrt{21}}{2}$
$\csc{t} = \dfrac{5 \sqrt{21}}{21}$
$\sec{t} =-\dfrac{5}{2}$
$\cot{t} =-\dfrac{2\sqrt{21}}{21}$
Work Step by Step
With $P= \left(-\dfrac{2}{5},\dfrac{\sqrt{21}}{5} \right) = (x,y)$, then $x = -\dfrac{2}{5}, \text{ and } \hspace{15pt} y =\dfrac{\sqrt{21}}{5}$.
Thus,
$\sin{t} = y$
$ \sin{t} = \dfrac{\sqrt{21}}{5}$
$\cos{t} = x$
$ \cos{t} = -\dfrac{2}{5}$
$\tan{t} = \dfrac{y}{x}$
$\tan{t} = \dfrac{\dfrac{\sqrt{21}}{5}}{ -\dfrac{2}{5} } = -\dfrac{\sqrt{21}}{2}$
$\csc{t} = \dfrac{1}{y}$
$\csc{t} = \dfrac{1}{\dfrac{\sqrt{21}}{5}} = \dfrac{5 \sqrt{21}}{21}$
$\sec{t} = \dfrac{1}{x}$
$\sec{t} = \dfrac{1}{-\dfrac{2}{5}}= -\dfrac{5}{2}$
$\cot{t} = \dfrac{x}{y}$
$\cot{t} = \dfrac{-\dfrac{2}{5} }{\dfrac{\sqrt{21}}{5}} = -\dfrac{2\sqrt{21}}{21}$