Answer
$\sin\theta=\frac{y}{r}=\frac{-1}{3}$
$\cos\theta=\frac{x}{r}=\frac{\sqrt 8}{3}$
$\tan\theta=\frac{y}{x}=\frac{-1 }{\sqrt 8}=\frac{-\sqrt 2}{4}$
$\cot\theta=\frac{x}{y}=\frac{\sqrt 8}{-1}=-2\sqrt 2$
$\sec\theta=\frac{r}{x}=\frac{3}{\sqrt 8}=\frac{3\sqrt 2}{4}$
$\csc\theta=\frac{r}{y}=\frac{3}{-1}=-3$
Work Step by Step
1. x positive, because cos is positive; and y is negative because csc is negative
y=-1 and r=3
2. Calculate x using distance formula
$3=\sqrt {(x)^{2}+(1)^{2}}$
$9=1+x^{2}$
$x=\sqrt {8}$
3. Plug those values to get final answer
$\sin\theta=\frac{y}{r}=\frac{-1}{3}$
$\cos\theta=\frac{x}{r}=\frac{\sqrt 8}{3}$
$\tan\theta=\frac{y}{x}=\frac{-1 }{\sqrt 8}=\frac{-\sqrt 2}{4}$
$\cot\theta=\frac{x}{y}=\frac{\sqrt 8}{-1}=-2\sqrt 2$
$\sec\theta=\frac{r}{x}=\frac{3}{\sqrt 8}=\frac{3\sqrt 2}{4}$
$\csc\theta=\frac{r}{y}=\frac{3}{-1}=-3$
