Chapter 4, Problem 5PS

To determine

To graph: Sketch the graph of the mentioned trigonometric function and decide whether it is even or odd function.

Explanation of Solution

Given information:

Mentioned function is f $\left(x\right)$ = ${\cos }^{2}x$ .

Graph:

The graph provided below is of cos2x .

The graph is plotted in real number line x axis and y axis.

  

Interpretation:

The following information of graph sketched above is provided below:-

Since the graph of cosx is provided below.

The graph is plotted in real number line x axis and y axis.

The graph is symmetric about the origin.

  

Therefore on square the given function,the graph will disappear from third and fourth quadrant .

The graph of cos2x is provided below:-

  

The graph is plotted on real number line x axis and y axis

Since we know that for even function $f\left(-x\right)=f\left(x\right)$ .

Therefore ${\cos }^2\left(-x\right)={\cos }^2\left(x\right)$

So,

  ${\cos }^{2}x$ is an even function.