Answer
$\sin\theta =\displaystyle \frac{8}{17}$
$\cos\theta =-\displaystyle \frac{15}{17}$
$\tan\theta =-\displaystyle \frac{8}{15}$
$\cot\theta =-\displaystyle \frac{15}{8}$
$\sec\theta =-\displaystyle \frac{17}{15}$
$\csc\theta =\displaystyle \frac{17}{8}$
Work Step by Step
For any real number $s$ represented by a directed arc on the unit circle,
$\sin s=y\quad \cos s=x \quad \displaystyle \tan s=\frac{y}{x} (x\neq 0)$
$\displaystyle \csc s=\frac{1}{y} (y\neq 0)\quad \displaystyle \sec s=\frac{1}{x} (x\neq 0) \displaystyle \quad\cot s=\frac{x}{y} (y\neq 0)$.
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$\displaystyle \sin\theta=y=\frac{8}{17}$
$\displaystyle \cos\theta=x=-\frac{15}{17}$
$\displaystyle \tan\theta=\frac{y}{x}=\frac{\frac{8}{17}}{-\frac{15}{17}}=\frac{8}{17}(-\frac{17}{15})=-\frac{8}{15}$
$\displaystyle \cot\theta=\frac{x}{y}=\frac{-\frac{15}{17}}{\frac{8}{17}}=-\frac{15}{17}(\frac{17}{8})=-\frac{15}{8}$
$\displaystyle \sec\theta=\frac{1}{x}=\frac{1}{-\frac{15}{17}}=-\frac{17}{15}$
$\displaystyle \csc\theta=\frac{1}{y}=\frac{1}{\frac{8}{17}}=\frac{17}{8}$
