Chapter 6, Problem 4CLT

To determine

The graph of the function. (Include two full periods.)

Answer to Problem 4CLT

The trigonometric function is plotted.

Explanation of Solution

Given info:

  $f(x)=3-2\sin \pi x$

Formula used:

Period of trigonometric functions

  $\begin{array}{l}\text{sin}\theta =2\pi \\ \text{cos}\theta =2\pi \\ \text{csc}\theta =2\pi \\ \text{sec}\theta =2\pi \\ \text{tan}\theta =\pi \\ \text{cot}\theta =2\pi \end{array}$

Calculation:

Given that $f(x)=3-2\sin \pi x$

We haveperiod of $\text{sin}\theta =2\pi$

That is

  $\begin{array}{l}\text{period of sin}\pi x=2\pi \\ \text{period of sin}x=2\end{array}$

Graph is given by

  

Conclusion:

Thus,the trigonometric function is plotted.