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 $t=210^\circ$, the terminal side is in quadrant III and $30^\circ$ to the $-x$-axis , we have:
$sin(t)=y=-\frac{1}{2}$,
$cos(t)=x=-\frac{\sqrt 3}{2}$,
$tan(t)=\frac{y}{x}=\frac{\sqrt 3}{3}$,
$cot(t)=\frac{x}{y}=\sqrt 3$,
$sec(t)=\frac{1}{x}=-\frac{2\sqrt 3}{3}$,
$csc(t)=\frac{1}{y}=-2$.
