/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 27 Determine the amplitude, period,... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 27

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=3 \sin (\pi x+2)$$

Short Answer

Expert verified
The amplitude is 3, the period is 2, and the phase shift is \(-2/\pi\).

Step by step solution

01

Determine the Amplitude

The amplitude is the coefficient of the sine function. In this case, the amplitude is 3. Hence, the amplitude is 3.
02

Determine the Period

The period can be obtained with the formula \(2\pi / \omega\) where \(\omega\) is the coefficient of x inside the sine function, which in this case is \(\pi\). Hence, subsituting \(\pi\) into the formula we have \(2\pi / \pi\) which simplifies to 2. Thus, the period is 2.
03

Determine the phase shift

The phase shift is determined by the constant being added or subtracted inside the function. Here, the constant is 2, so the phase shift is \(-2/ \pi\).
04

Graphing the function

To graph one period of the function, plot the sine curve starting from the phase shift, with the maximum and minimum values being equal to the amplitude and -amplitude, respectively. The period determines the length along the x-axis that the graph repeats.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use a graphing utility to graph two periodsof the function. Use a graphing utility to graph Use a graphing utility to graph \( y=\sin x-\frac{\sin 3 x}{9}+\frac{\sin 5 x}{25} \) in a \(\left[-2 \pi, 2 \pi, \frac{\pi}{2}\right]\) by \([-2,2,1]\) viewing rectangle. How do these waves compare to the smooth rolling waves of the basic sine curve?

a. Graph the restricted cotangent function, \(y=\cot x,\) by restricting \(x\) to the interval \((0, \pi)\). b. Use the horizontal line test to explain why the restricted cotangent function has an inverse function. c. Use the graph of the restricted cotangent function to graph \(y=\cot ^{-1} x\).

Describe an angle in standard position.

a. Graph the restricted secant function, \(y=\sec x,\) by restricting \(x\) to the intervals \(\left[0, \frac{\pi}{2}\right)\) and \(\left(\frac{\pi}{2}, \pi\right]\) b. Use the horizontal line test to explain why the restricted secant function has an inverse function. c. Use the graph of the restricted secant function to graph \(y=\sec ^{-1} x\).

Have you ever noticed that we use the vocabulary of angles in everyday speech? Here is an example: My opinion about art museums took a \(180^{\circ}\) turn after visiting the San Francisco Museum of Modern Art. Explain what this means. Then give another example of the vocabulary of angles in everyday use.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.