Answer
$sin(t) =\frac{1}{2}$,
$cos(t) =\frac{\sqrt 3}{2}$,
$tan(t) =\frac{\sqrt 3}{3}$,
$cot(t) =\sqrt 3$,
$sec(t) =\frac{2\sqrt 3}{3}$,
$csc(t) =2$.
Work Step by Step
Given $t=\frac{13\pi}{6}=2\pi+\frac{\pi}{6}$, the terminal side is in quadrant I and $t_0=\frac{\pi}{6}$ to the $+x$-axis , we have:
$sin(t)=sin(t_0)=\frac{1}{2}$,
$cos(t)=cos(t_0)=\frac{\sqrt 3}{2}$,
$tan(t)=tan(t_0)=\frac{\sqrt 3}{3}$,
$cot(t)=cot(t_0)=\sqrt 3$,
$sec(t)=sec(t_0)=\frac{2\sqrt 3}{3}$,
$csc(t)=csc(t_0)=2$.
