Answer
$sin(t) =-\frac{2}{3}$,
$cos(t) =-\frac{\sqrt 5}{3}$,
$tan(t) =\frac{2\sqrt 5}{5}$,
$cot(t) =\frac{\sqrt 5}{2}$,
$sec(t) =-\frac{3\sqrt 5}{5}$,
$csc(t) =-\frac{3}{2}$.
Work Step by Step
Given $x=-\frac{\sqrt 5}{3}, y=-\frac{2}{3}, r=1$, we have:
$sin(t)=y=-\frac{2}{3}$,
$cos(t)=x=-\frac{\sqrt 5}{3}$,
$tan(t)=\frac{y}{x}=\frac{2\sqrt 5}{5}$,
$cot(t)=\frac{x}{y}=\frac{\sqrt 5}{2}$,
$sec(t)=\frac{1}{x}=-\frac{3\sqrt 5}{5}$,
$csc(t)=\frac{1}{y}=-\frac{3}{2}$.
