/*! 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 21 Determine the amplitude, period,... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 21

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

Short Answer

Expert verified
The amplitude of the function \(y = 3 \sin (2 x-\pi)\) is 3, its period is \(\pi\), and has a phase shift of -\(\frac{\pi}{2}\).

Step by step solution

01

Amplitude

The coefficient of the sine function gives the amplitude of the function. Here, the coefficient is 3, so the amplitude of the function \(y = 3 \sin (2 x-\pi)\) is 3.
02

Period

The period can be calculated using the formula \(T = \frac{2\pi}{|B|}\) where B is the coefficient of x. Here B = 2, hence the period \(T = \frac{2\pi}{2} = \pi\).
03

Phase Shift

Phase shift can be calculated by the formula \(-\frac{C}{B}\) where C is the constant term inside the function. Here, C is \(\pi\), B is 2, so the phase shift is \(-\frac{\pi}{2}\). It signifies the function graph to the right of origin.
04

Graph the function

To plot the function, first mark the amplitude on the y-axis and period on the x-axis. Then, shift the sine wave graph to the right by the phase shift amount. Plot the graph for one complete period. Now, the graph starts at -\(\frac{\pi}{2}\) (due to phase shift) and completes one cycle at \(\frac{\pi}{2}\), the height of wave (amplitude) is 3, and the function repeats this wave pattern every \(\pi\) units (period).

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

The angular speed of a point on Earth is \(\frac{\pi}{12}\) radian per hour. The Equator lies on a circle of radius approximately 4000 miles. Find the linear velocity, in miles per hour, of \(\overline{\mathbf{a}}\) point on the Equator.

A water wheel has a radius of 12 feet. The wheel is rotating at 20 revolutions per minute. Find the linear speed, in feet per minute, of the water.

Use a graphing utility to graph two periods of the function. $$y=3 \sin (2 x-\pi)+5$$

Without drawing a graph, describe the behavior of the graph of \(y=\cos ^{-1} x .\) Mention the function's domain and range in your description.

Use a graphing utility to graph two periods of the function. $$y=3 \sin (2 x+\pi)$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.