Answer
$sin(t) =-\frac{\sqrt 3}{2}$,
$cos(t) =-\frac{1}{2}$,
$tan(t) =\sqrt 3$,
$cot(t) =\frac{\sqrt 3}{3}$,
$sec(t) =-2$,
$csc(t) =-\frac{2\sqrt 3}{3}$.
Work Step by Step
Given $t=240^\circ$, the terminal side is in quadrant III and $60^\circ$ to the $-x$-axis , we have:
$sin(t)=y=-\frac{\sqrt 3}{2}$,
$cos(t)=x=-\frac{1}{2}$,
$tan(t)=\frac{y}{x}=\sqrt 3$,
$cot(t)=\frac{x}{y}=\frac{\sqrt 3}{3}$,
$sec(t)=\frac{1}{x}=-2$,
$csc(t)=\frac{1}{y}=-\frac{2\sqrt 3}{3}$.
