Answer
$ \sin{t} = -\dfrac{\sqrt{3}}{2}$
$ \cos{t} = \dfrac{1}{2}$
$\tan{t} =-\sqrt{3}$
$\csc{t} =-\dfrac{2\sqrt{3}}{3}$
$\sec{t} =2$
$\cot{t} =-\dfrac{\sqrt{3}}{3}$
Work Step by Step
With $P= \left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2} \right) = (x,y)$, then $x = \dfrac{1}{2}, \text{ and } \hspace{15pt} y =-\dfrac{\sqrt{3}}{2}$.
Thus,
$\sin{t} = y$
$ \sin{t} = -\dfrac{\sqrt{3}}{2}$
$\cos{t} = x$
$ \cos{t} = \dfrac{1}{2}$
$\tan{t} = \dfrac{y}{x}$
$\tan{t} = \dfrac{-\dfrac{\sqrt{3}}{2}}{ \dfrac{1}{2}} = -\sqrt{3}$
$\csc{t} = \dfrac{1}{y}$
$\csc{t} = \dfrac{1}{-\dfrac{\sqrt{3}}{2}} = -\dfrac{2\sqrt{3}}{3}$
$\sec{t} = \dfrac{1}{x}$
$\sec{t} = \dfrac{1}{\dfrac{1}{2}}= 2$
$\cot{t} = \dfrac{x}{y}$
$\cot{t} = \dfrac{\dfrac{1}{2}}{-\dfrac{\sqrt{3}}{2}} = -\dfrac{\sqrt{3}}{3}$
