Chapter 7.5, Problem 63E

To determine

To find: a numerical value of one trigonometric function of x .

Answer to Problem 63E

  $\sin x=\frac{\sqrt{2}}{5}$

Explanation of Solution

Given information:

  $\frac{\tan x}{\sec x}=\frac{\sqrt{2}}{5}$

Calculation:

The value of trigonometric function of x can be evaluated as follows:

  $\begin{array}{c}\frac{\tan x}{\sec x}=\frac{\sqrt{2}}{5}\end{array}$

  $\begin{array}{c}\frac{\frac{\sin x}{\cos x}}{\frac{1}{\cos x}}=\frac{\sqrt{2}}{5}\left[\text{Using reciprocal and quotient identities}\right]\end{array}$

  $\begin{array}{c}\left(\frac{\sin x}{\cos x}\right)\left(\cos x\right)=\frac{\sqrt{2}}{5}\end{array}$

  $\begin{array}{c}\sin x=\frac{\sqrt{2}}{5}\end{array}$

Thus the numerical value of one trigonometric function of x is $\sin x=\frac{\sqrt{2}}{5}$ .