Chapter 12.1, Problem 1GP

To determine

To find the values of the six trigonometric for angle B.

Explanation of Solution

Given:

The given right triangle is-

  

Calculation:

Using the law of sines-

  

  $\begin{array}{l}\sin B=\frac{AC}{AB}=\frac{4}{5}\\ \cos B=\frac{BC}{AB}=\frac{3}{5}\\ \tan B=\frac{AC}{BC}=\frac{4}{3}\end{array}$

  $\begin{array}{l}\cot B=\frac{BC}{AC}=\frac{3}{4}\\ \sec B=\frac{AB}{BC}=\frac{5}{3}\\ \cos ecB=\frac{AB}{AC}=\frac{5}{4}\end{array}$