Answer
$\sin\theta=\frac{y}{r}=\frac{15}{17}$
$\cos\theta=\frac{x}{r}=\frac{-8}{17}$
$\tan\theta=\frac{y}{x}=\frac{15}{-8}$
$\cot\theta=\frac{x}{y}=\frac{-8}{15}$
$\sec\theta=\frac{r}{x}=\frac{17}{-8}$
$\csc\theta=\frac{r}{y}=\frac{17}{15}$
Work Step by Step
1. The angle is in the Quadrant II, then x is negative and y is positive.
$x=-8$
$y=15$
2. Then calculate r, using x, y and distance formula
$r=\sqrt {(-8)^{2}+(15)^{2}} =\sqrt {289}=17$
3. Then when you have all values you need just insert them to find trig functions
$\sin\theta=\frac{y}{r}=\frac{15}{17}$
$\cos\theta=\frac{x}{r}=\frac{-8}{17}$
$\tan\theta=\frac{y}{x}=\frac{15}{-8}$
$\cot\theta=\frac{x}{y}=\frac{-8}{15}$
$\sec\theta=\frac{r}{x}=\frac{17}{-8}$
$\csc\theta=\frac{r}{y}=\frac{17}{15}$
