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