Answer
$sin(t) =-\frac{\sqrt 2}{2}$,
$cos(t) =-\frac{\sqrt 2}{2}$,
$tan(t) =1$,
$cot(t) =1$,
$sec(t) =-\sqrt 2$,
$csc(t) = -\sqrt 2$.
Work Step by Step
Given $t=-135^\circ$, the terminal side is in quadrant III and $t_0=45^\circ$ to the $-x$-axis , we have:
$sin(t)=-sin(t_0)=-\frac{\sqrt 2}{2}$,
$cos(t)=-cos(t_0)=-\frac{\sqrt 2}{2}$,
$tan(t)=tan(t_0)=1$,
$cot(t)=cot(t_0)=1$,
$sec(t)=-sec(t_0)=-\sqrt 2$,
$csc(t)=-csc(t_0)= -\sqrt 2$.
