/*! 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 3 Determine the amplitude of each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 3

Determine the amplitude of each function. Then graph the function and \(y=\sin x\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi\). $$y=\frac{1}{3} \sin x$$

Short Answer

Expert verified
The amplitude of the function \(y=\frac{1}{3} \sin x\) is \(\frac{1}{3}\), which means that its graph will reach peak and dip of \(\frac{1}{3}\) only, compared to the graph of \(y=\sin x\).

Step by step solution

01

Observing the function

Observe that given function is \(y=\frac{1}{3} \sin x\). This is a sine function where coefficient of \(\sin x\) is \(\frac{1}{3}\). Recall that for any function \(y=a \sin x\), the value of \(a\) is the amplitude.
02

Finding the amplitude

The amplitude of the given function is \(\frac{1}{3}\).
03

Comparing to normal sine function

Now, compare it with the function \(y = \sin x\). For \(y = \sin x\), the amplitude is 1, as there is no coefficient in front of the \(\sin x\). This means that the given function will reach only a third of the height of the \(y = \sin x\) at its peak and dip.
04

Drawing the graph

Plot the graphs of \(y=\frac{1}{3} \sin x\) and \(y= \sin x\) for the range \(0 \leq x \leq 2 \pi\). Note that both graphs will fluctuate between their amplitude values and demonstrate standard sine wave behavior. The wave of \(y=\frac{1}{3} \sin x\) will be shorter due to its lower amplitude.

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 vertical shift to graph one period of the function. $$y=2 \sin \frac{1}{2} x+1$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A ride on a circular Ferris wheel is like riding sinusoidal graphs.

Graph \(y=\sin \frac{1}{x}\) in a [-0.2,0.2,0.01] by [-1.2,1.2,0.01] viewing rectangle. What is happening as \(x\) approaches 0 from the left or the right? Explain this behavior.

The toll to a bridge costs \(\$ 8.00 .\) Commuters who frequently use the bridge have the option of purchasing a monthly discount pass for \(\$ 36.00 .\) With the discount pass, the toll is reduced to \(\$ 5.00 .\) For how many bridge crossings per month will the cost without the discount pass be the same as the cost with pass? What will be the monthly cost for each option? (Section P.8, Example 3)

Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$30.42^{\circ}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.