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 $t=\frac{5\pi}{6}$, the terminal side is in quadrant II and $\frac{\pi}{6}$ to the $-x$-axis , we have:
$sin(t)=y=\frac{1}{2}$,
$cos(t)=x=-\frac{\sqrt 3}{2}$,
$tan(t)=\frac{y}{x}=-\frac{\sqrt 3}{3}$,
$cot(t)=\frac{x}{y}=-\sqrt 3$,
$sec(t)=\frac{1}{x}=-\frac{2\sqrt 3}{3}$,
$csc(t)=\frac{1}{y}=2$.
