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 $t=-\frac{\pi}{6}$, the terminal side is in quadrant IV and $t_0=\frac{\pi}{6}$ to the $+x$-axis , we have:
$sin(t)=-sin(t_0)=-\frac{1}{2}$,
$cos(t)=cos(t_0)=\frac{\sqrt 3}{2}$,
$tan(t)=-tan(t_0)=-\frac{\sqrt 3}{3}$,
$cot(t)=-cot(t_0)=-\sqrt 3$,
$sec(t)=sec(t_0)=\frac{2\sqrt 3}{3}$,
$csc(t)=-csc(t_0)= -2$.
