Chapter 4.5, Problem 82E

To determine

To find: real numbers $x$ such that $y_1=y_2$ in $\left[-2\pi ,2\pi \right]$ .

Answer to Problem 82E

  $x=3.14$ or y1 $x=-3.14$ .

Explanation of Solution

Given information:

Given equation

  $y_1=\cos x,y_2=-1$ .

Calculation:

Given

  $y_1=\cos x,y_2=-1$ .

Now, let us sketch the graph of the two functions in the interval $\left[-2\pi ,2\pi \right]$ .

To plot both the graph together on same axis, follows the steps given below:

Press the button $Y=$ and type $y_1=\cos x$ and $y_2=-1$

  

Press the button WINDOW and adjust the window as shown:

  

Press the button TRACE or GRAPH to obtain the graph.

  

Now, press the button 2^nd CALC. Select option “5”

  

Move cursor on to $Y_1$ using arrow key and press ENTER

  

Now move cursor on to $Y_2$ and press ENTER

  

Move cursor near point of intersection of graph on right and press ENTER

  

It will show following coordinates.

  

Repeat above procedure to find point of intersection on left.

It will show following coordinates.

  

Hence, $y_1=y_2$ when $x=3.14$ or $x=-3.14$ .