Chapter 14.8, Problem 15WE

To determine

To find:the solution of the given trigonometric function.

Answer to Problem 15WE

  $x={0.32}^{\circ }$

Explanation of Solution

Given:

The given trigonometric function is $3\sec x=\csc x$ .

Calculation:

As thegiven trigonometric function is $3\sec x=\csc x$ .

Now, to solve the given trigonometric function. Therefore,

  $\begin{array}{l}3\sec x=\csc x\{\text{given equation}}\\ \therefore \frac{3}{\cos x}=\frac{1}{\sin x}\{\text{inverse trigonometry property}}\\ \text{3}\sin x=\cos x\{\text{cross-multiplication}}\\ 3\frac{\sin x}{\cos x}=\frac{\cos x}{\cos x}\{\text{divide both sides by }\cos \theta \text{}}\\ \tan x=\frac{1}{3}\\ \therefore x={0.32}^{\circ }\end{array}$

Hence, the solution of the given trigonometric function is $x={0.32}^{\circ }$ .