Chapter 4.5, Problem 49E

Solution

To calculate: The approximate solution for the equation $\sec x=5\cos x$ in the interval $-\pi <x<\pi$ .

The approximate solution for the equation $\sec x=5\cos x$ in the interval $-\pi <x<\pi$ is $x\approx \pm 1.107$ or $x\approx \pm 2.034$ .

Given information:

The equation $\sec x=5\cos x$ in the interval $-\pi <x<\pi$ .

Formula used :

Use the graphical method to find the solution.

Calculation:

Consider the equation $\sec x=5\cos x$ ,

Subtract $5\cos x$ from both sides.

  $\begin{array}{c}\sec x-5\cos x=5\cos x-5\cos x\\ \sec x-5\cos x=0\end{array}$

Use TI-83 calculator to find the solution.

Put the calculator in RADIAN mode.

Put the equation as $y=\frac{1}{\cos x}-5\cos x$ .

Set up the window for the variables.

  

Graph the function.

  

  

  

  

It can be seen that the graph attains value of $y=0$ at $x\approx \pm 1.107$ or $x\approx \pm 2.034$ .

Thus, the approximate solution for the equation $\sec x=5\cos x$ in the interval $-\pi <x<\pi$ is $x\approx \pm 1.107$ or $x\approx \pm 2.034$ .