Chapter 14.8, Problem 7WE

To determine

To find:the solution of the given trigonometric function.

Answer to Problem 7WE

  $\theta ={14.5}^{\circ }$

Explanation of Solution

Given:

The given trigonometric function is $\csc \theta =16\sin \theta$ .

Calculation:

As thegiven trigonometric function is $\csc \theta =16\sin \theta$ .

Now, to solve the given trigonometric function. Therefore,

  $\begin{array}{l}\csc \theta =16\sin \theta \{\text{given equation}}\\ \therefore \frac{1}{\sin \theta }=16\sin \theta \{\text{inverse trigonometry property}}\\ {\text{16sin}}^2\theta =1\{\text{cross-multiplication}}\\ {\text{sin}}^2\theta =\frac{1}{16}\{\text{divide both sides by }16\text{}}\\ \text{sin}\theta =\pm \sqrt{\frac{1}{16}}\{\text{taking square root both sides}}\\ \text{sin}\theta =\pm \frac{1}{4}\\ \theta ={14.5}^{\circ }\end{array}$

Hence, the solution of the given trigonometric function is $\theta ={14.5}^{\circ }$ .