/*! 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 59 Use a vertical shift to graph on... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 59

Use a vertical shift to graph one period of the function. $$y=-3 \cos 2 \pi x+2$$

Short Answer

Expert verified
The function has amplitude 3, period 1 and vertical shift 2 and it starts at its lowest point due to the negative coefficient of cosine. By marking these points on the graph, we sketch one period.

Step by step solution

01

Identify Parameters

The given function is \(y=-3 \cos 2 \pi x +2 \). By comparing to the standard cosine function \(y=a \cos (b x) +c\), we can observe that a=-3, b=2\pi, and c=2. The value of 'a' affects the amplitude, 'b' affects the period and 'c' is the vertical shift.
02

Define Amplitude and Period

Calculate the amplitude and period. The amplitude is the absolute value of 'a', so here, the amplitude is | -3 |=3. The period is given by \(\frac{2\pi}{|b|}\), so here the period is \(\frac{2\pi}{|2\pi|}\) = 1.
03

Define the Vertical Shift

The vertical shift is given by the constant 'c', which is 2 in this case. This means our function shifts up by 2 units.
04

Graph the function

To graph, we start by marking the period on the x-axis, which is 1. Mark the shifted midline on the y-axis, it's 2. Since it's a negative cosine function, start at the lowest point, which is 2 - amplitude = -1. The function will reach its highest point at x=0.5, so we mark the harmonious points for one complete 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

Graph each pair of functions in the same viewing rectangle. Use your knowledge of the domain and range for the inverse trigonometric function to select an appropriate viewing rectangle. How is the graph of the second equation in cach exercise related to the graph of the first equation? $$ y=\sin ^{-1} x \text { and } y=\sin ^{-1} x+2 $$

Use a sketch to find the exact value of each expression. $$ \sin \left[\tan ^{-1}\left(-\frac{3}{4}\right)\right] $$

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 \(x\). $$ \sec \left(\cos ^{-1} \frac{1}{x}\right) $$

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Using the equation \(y=A \sin B x,\) if 1 replace either \(A\) or \(B\) with its opposite, the graph of the resulting equation is a reflection of the graph of the original equation about the \(x\) -axis.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

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.