Chapter 13.4, Problem 33WE

To determine

To Graph: The functions. Show at least two periods.

Explanation of Solution

Given: $y=\frac{1}{2}sin2\pi x$

Given: $y=\frac{1}{2}sin2\pi x$

The function is in the form of

  $y=a\sin bx$

For function $y=sin2\pi x$ .

Maximum and minimum values are $1and-1.$

Period of the function is

  $\begin{array}{l}y=\frac{2\pi }{b}\\ y=\frac{2\pi }{2\pi }=1\end{array}$

  

The graph of the function $y=\frac{1}{2}sin2\pi x$ is shown below.

  

The maximum and minimum values of the functions are $\frac{1}{2}and-\frac{1}{2}$ .

The period of the function is $1$ .