Chapter 6.1, Problem 58E

To determine

Tofind:The remaining trigonometric function.

Explanation of Solution

Given: The given data is, $\tan \theta =-\frac{8}{15}$ and $\csc \theta =\frac{17}{8}$

The sine function is calculated as,

  $\begin{array}{c}\sin \theta =\frac{1}{\csc \theta }\\ =\frac{1}{17/8}\\ =\frac{8}{17}\end{array}$

The cos function s calculated as,

  $\begin{array}{c}\tan \theta =\frac{\sin \theta }{\cos \theta }\\ \cos \theta =\frac{\sin \theta }{\tan \theta }\\ =\frac{8/17}{-8/15}\\ =\frac{-15}{17}\end{array}$

The cot function is calculated as,

  $\begin{array}{c}\cot \theta =\frac{1}{\tan \theta }\\ =\frac{1}{-8/15}\\ =\frac{-15}{8}\end{array}$

The sec function is calculated as,

  $\begin{array}{c}\sec \theta =\frac{1}{\cos \theta }\\ =\frac{1}{-15/17}\\ =\frac{17}{15}\end{array}$

Therefore, the other trigonometric function are listed above.