Question

complete the table. determine the exact values of the six trigonometric functions of the angles. let the given examples serve as your guide.: a. (-8/17, 15/17) b. (12/13, -5/13) given sin θ cos θ tan θ csc θ sec θ a. 15/17 b.

Explanation:

Step1: Recall trigonometric function definitions

For a point $(x,y)$ on the unit - circle, $\cos\theta=x$, $\sin\theta = y$, $\tan\theta=\frac{y}{x}(x
eq0)$, $\csc\theta=\frac{1}{y}(y
eq0)$, $\sec\theta=\frac{1}{x}(x
eq0)$, $\cot\theta=\frac{x}{y}(y
eq0)$.

Step2: For part a

Given the point $(-\frac{8}{17},\frac{15}{17})$ on the unit - circle.
$\cos\theta=-\frac{8}{17}$, $\tan\theta=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8}$, $\csc\theta=\frac{1}{\frac{15}{17}}=\frac{17}{15}$, $\sec\theta=\frac{1}{-\frac{8}{17}}=-\frac{17}{8}$, $\cot\theta=-\frac{8}{15}$.

Step3: For part b

Given the point $(\frac{12}{13},-\frac{5}{13})$ on the unit - circle.
$\sin\theta=-\frac{5}{13}$, $\cos\theta=\frac{12}{13}$, $\tan\theta=\frac{-\frac{5}{13}}{\frac{12}{13}}=-\frac{5}{12}$, $\csc\theta=\frac{1}{-\frac{5}{13}}=-\frac{13}{5}$, $\sec\theta=\frac{1}{\frac{12}{13}}=\frac{13}{12}$, $\cot\theta=-\frac{12}{5}$.

Answer:

Given	$\sin\theta$	$\cos\theta$	$\tan\theta$	$\csc\theta$	$\sec\theta$	$\cot\theta$
b.	$-\frac{5}{13}$	$\frac{12}{13}$	$-\frac{5}{12}$	$-\frac{13}{5}$	$\frac{13}{12}$	$-\frac{12}{5}$