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