Chapter 8.6, Problem 6CE

To determine

To express $\sin B,\cos B\text{and}\tan B$ as fractions by using the triangle shown below.

  

Answer to Problem 6CE

  $\sin B=\frac{b}{c},\cos B=\frac{a}{c}\&\tan B=\frac{b}{a}$

Explanation of Solution

Given:

  

Calculation:

In the given triangle,

  $\begin{array}{l}\sin B=\frac{\text{opposite}}{\text{hypotenuse}}\\ =\frac{b}{c}\\ \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}\\ =\frac{a}{c}\\ \tan B=\frac{\text{opposite}}{\text{adjacent}}\\ =\frac{b}{a}\end{array}$