Chapter 4.6, Problem 54E

To determine

To find: the solutions of the equation in the interval $\left[-2\pi ,2\pi \right]$ .

Answer to Problem 54E

Solution set is, $x=\left\{-5.23,-1.05,1.05,5.23\right\}$ .

Explanation of Solution

Given information:

Given function is

  $\sec x=2$ .

Calculation:

Consider,

  $\tan x=\sqrt{3}$

To plot the graph in $TI-83$ , proceed as below:

Press the button Y= and type $y_1=\frac{1}{\cos x}$ and $y_2=2$

  

Press the button WINDOW to adjust the graphing window as shown:

  

Press the button TRACE or GRAPH to obtain the graph:

  

Now, to find the intersection point, press the button 2^nd CALC

Select option”5”

  

Move cursor on $Y_1$ curve and press ENTER

  

Move cursor on $Y_2$ curve and press ENTER

  

Move cursor near point of intersection of graphs and press ENTER

  

It will show following coordinates.

  

Repeat above procedure to find other points ofof intersection. Then the results will be:

  

Hence solution set is, $x=\left\{-5.23,-1.05,1.05,5.23\right\}$