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 $t=\frac{8\pi}{3}=2\pi+\frac{2\pi}{3}$, the terminal side is in quadrant II and $t_0=\frac{\pi}{3}$ to the $-x$-axis , we have:
$sin(t)=sin(t_0)=\frac{\sqrt 3}{2}$,
$cos(t)=-cos(t_0)=-\frac{1}{2}$,
$tan(t)=-tan(t_0)=-\sqrt 3$,
$cot(t)=-cot(t_0)=-\frac{\sqrt 3}{3}$,
$sec(t)=-sec(t_0)=-2$,
$csc(t)=csc(t_0)=\frac{2\sqrt 3}{3}$.
