/*! 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 55 Use a vertical shift to graph on... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 55

Use a vertical shift to graph one period of the function. $$y=\cos x-3$$

Short Answer

Expert verified
The given function \(y=\cos x - 3\) is a vertical shift of the cosine function, where the entire graph of the basic cosine function is moved 3 units downwards.

Step by step solution

01

Understand the Basic Cosine Function

The basic cosine function \(y=\cos x\) has a period of \(2 \pi\), and wave amplitude of 1. It reaches its maximum value at \(x=0\) (and multiples of \(2 \pi\)) and minimum values at \(x=\pi\) (and multiples of \(2 \pi\)).
02

Understanding the Impact of -3 on the Cosine Function

The -3 at the end of the function \(y=\cos x - 3\) indicates a vertical shift of the cosine function downwards by 3 units on the y-axis. The wave amplitude remains the same as the basic cosine function, at 1. So, the existing minimum and maximum values for the function will be shifted down by 3 units.
03

Graphing the Function

To graph this function, first draw the basic cosine function. Then, translate the graph 3 units downwards. The maximum of the function will now be at \(y=1-3=-2\), and the minimum of the function will be at \(y=-1-3=-4\).

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

Repeat Exercise 109 for data of your choice. The data can involve the average monthly temperatures for the region where you live or any data whose scatter plot takes the form of a sinusoidal function.

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\tan 4 x$$

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?

Describe a relationship between the graphs of \(y=\sin x\) and \(y=\cos x\)

Rounded to the nearest hour, Los Angeles averages 14 hours of daylight in June, 10 hours in December, and 12 hours in March and September. Let \(x\) represent the number of months after June and let \(y\) represent the number of hours of daylight in month \(x .\) Make a graph that displays the information from June of one year to June of the following year.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.