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