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 $t=-\frac{14\pi}{3}=-4\pi-\frac{2\pi}{3}$, the terminal side is in quadrant III with $t_0=\frac{2\pi}{3}$ to the $-x$-axis , we have:
$sin(t)=-sin(t_0)=-\frac{\sqrt 3}{2}$,
$cos(t)=-cos(t_0)=-\frac{1}{2}$,
$tan(t)=tan(t_0)=\sqrt 3$,
$cot(t)=cot(t_0)=\frac{\sqrt 3}{3}$,
$sec(t)=-sec(t_0)=-2$,
$csc(t)=-csc(t_0)=-\frac{2\sqrt 3}{3}$.
