Answer
$\sin\theta=\frac{y}{r}=\frac{8}{\sqrt {67}}=\frac{8\sqrt {67}}{67}$
$\cos\theta=\frac{x}{r}=\frac{\sqrt {3}}{\sqrt{67}}=\frac{\sqrt {201}}{67}$
$\tan\theta=\frac{y}{x}=\frac{8 }{\sqrt {3}}=\frac{8\sqrt {3} }{3}$
$\cot\theta=\frac{x}{y}=\frac{\sqrt {3}}{8}$
$\sec\theta=\frac{r}{x}=\frac{\sqrt {67}}{\sqrt {3}}=\frac{\sqrt {201}}{3}$
$\csc\theta=\frac{r}{y}=\frac{\sqrt {67}}{8}$
Work Step by Step
1. I quadrant x and y are positive
$x=\sqrt 3$ and $y=8$
2. Calculate r using distnace formula
$r=\sqrt {(\sqrt 3)^{2}+(8)^{2}} =\sqrt {67}$
3. Plug the values to find trig function
$\sin\theta=\frac{y}{r}=\frac{8}{\sqrt {67}}=\frac{8\sqrt {67}}{67}$
$\cos\theta=\frac{x}{r}=\frac{\sqrt {3}}{\sqrt{67}}=\frac{\sqrt {201}}{67}$
$\tan\theta=\frac{y}{x}=\frac{8 }{\sqrt {3}}=\frac{8\sqrt {3} }{3}$
$\cot\theta=\frac{x}{y}=\frac{\sqrt {3}}{8}$
$\sec\theta=\frac{r}{x}=\frac{\sqrt {67}}{\sqrt {3}}=\frac{\sqrt {201}}{3}$
$\csc\theta=\frac{r}{y}=\frac{\sqrt {67}}{8}$
