Chapter 4, Problem 6PS

To determine

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

Explanation of Solution

Given information:

Given function is $f\left(x\right)$ = $si{n}^{2}x$ .

Graph:

The graph provided below is of sin2x .

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

  

Interpretation:

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

Since the graph of sinx 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 sin2x is provided below:-

  

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

Since we know that forevenfunction,

  $f\left(-x\right)=f\left(x\right)$ .

And for odd function,

  $f\left(-x\right)=-f\left(x\right)$ .

Therefore,

  ${\sin }^2\left(-x\right)={\sin }^2\left(x\right)$ .

So,

  ${\sin }^{2}x$ is an even function.