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 $t=405^\circ=360^\circ+45^\circ$, the terminal side is in quadrant I and $t_0=45^\circ$ to the $+x$-axis , we have:
$sin(t)=sin(t_0)=\frac{\sqrt 2}{2}$,
$cos(t)=cos(t_0)=\frac{\sqrt 2}{2}$,
$tan(t)=tan(t_0)=1$,
$cot(t)=cot(t_0)=1$,
$sec(t)=sec(t_0)=\sqrt 2$,
$csc(t)=csc(t_0)=\sqrt 2$.
