/*! 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 5: Problem 55

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

Short Answer

Expert verified
The graph of the function \(y = \cos x - 3\) is a cosine wave that oscillates between -2 and -4 with a period of \(2蟺\), centered around \(y = -3\).

Step by step solution

01

Understanding the basic cosine function graph

Start with the fundamental graph of \(y = \cos x\). It's a wave that oscillates between -1 and 1, with a period of \(2蟺\) (meaning it repeats every \(2蟺\) units).
02

Applying the vertical shift

The function \(y = \cos x - 3\) is a regular cosine function, but it's shifted down by 3 units. That implies every point on the \(y = \cos x\) graph will be moved three units downwards to get the graph of \(y = \cos x - 3\). This shifting doesn't affect the shape or the period of the cosine function; it only changes the location of the graph.
03

Graphing the function

First, draw the basic cosine function. Then, move each point on the graph three units down. Another perspective is to think of the center line of the wave as being at \(y = -3\) instead of the x-axis. The wave still oscillates 1 unit above and below this center line, meaning it reaches a maximum of \( -3 + 1 = -2\) and a minimum of \(-3 - 1 = -4\) within each 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

We will prove the following identities: $$\begin{array}{l} {\sin ^{2} x=\frac{1}{2}-\frac{1}{2} \cos 2 x} \\ {\cos ^{2} x=\frac{1}{2}+\frac{1}{2} \cos 2 x} \end{array}$$ Use the identity for \(\sin ^{2} x\) to graph one period of \(y=\sin ^{2} x\)

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 \(y=\cot ^{-1} x\).

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \cos \left(\sin ^{-1} \frac{1}{x}\right) $$

Determine the domain and the range of each function. $$ f(x)=\sin \left(\sin ^{-1} x\right) $$

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \sec \left(\cos ^{-1} \frac{1}{x}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

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.