Answer
$sin\theta =\frac{\sqrt 5}{5}$,
$cos\theta =\frac{2\sqrt 5}{5}$,
$tan\theta =\frac{1}{2}$,
$cot\theta =2$,
$sec\theta =\frac{\sqrt 5}{2}$,
$csc\theta = \sqrt 5 $.
Work Step by Step
Let $x=6,y=3$, we have $r=\sqrt {6^2+3^2}=3\sqrt 5$, thus
$sin\theta=\frac{y}{r}=\frac{\sqrt 5}{5}$,
$cos\theta=\frac{x}{r}=\frac{2\sqrt 5}{5}$,
$tan\theta=\frac{y}{x}=\frac{1}{2}$,
$cot\theta=\frac{x}{y}=2$,
$sec\theta=\frac{r}{x}=\frac{\sqrt 5}{2}$,
$csc\theta=\frac{r}{y}= \sqrt 5 $.
