/*! 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 17 $$\text {Graph each function ove... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 17

$$\text {Graph each function over the interval }[-2 \pi, 2 \pi] . \text { Give the amplitude.}$$ $$y=-\cos x$$

Short Answer

Expert verified
Amplitude is 1. Reflect cosine curve over x-axis from \([-2\text{pi}, 2\text{pi}]\).

Step by step solution

01

Identify the function

The given function is \(y = -\cos x\). This is a cosine function that has been reflected over the x-axis.
02

Determine the amplitude

The amplitude of a cosine function \(\text{y} = \text{a} \cos(\text{bx} + \text{c}) + \text{d}\) is given by the absolute value of 'a'. Here, 'a' is \-1 so the amplitude is \(\left| -1 \right| = 1\).
03

Set up the interval

The function needs to be graphed over the interval \([-2\pi, 2\text{pi}]\). This creates a symmetric interval around the origin.
04

Determine key points

For the cosine function \(y = -\cos x\), evaluate key points: 1. At \(x = -2\text{pi}\), \(y = \cos(-2\text{pi}) = 1\) so \(y = -1\).2. At \(x = -\text{pi}\), \(y = \cos(-\text{pi}) = -1\) so \(y = 1\).3. At \(x = 0\), \(y = \cos(0) = 1\) so \(y = -1\).4. At \(x = \text{pi}\), \(y = \cos(\text{pi}) = -1\) so \(y = 1\).5. At \(x = 2\text{pi}\), \(y = \cos(2\text{pi}) = 1\) so \(y = -1\).
05

Sketch the graph

Using the key points, sketch the graph for \(y = -\cos x\) from \(x = -2\text{pi}\) to \(x = 2\text{pi}\). The graph will reflect the typical cosine curve over the x-axis, with a maximum at \(y = 1\) and a minimum at \(y = -1\).
06

Label the amplitude

Clearly label the amplitude of the graph as 1, which is the maximum vertical distance from the middle of the wave to the peak.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

cosine function
The function given in the exercise is a cosine function, expressed as \(y = -\text{cos}\text{x}\). In trigonometry, the cosine function is one of the basic periodic functions. The standard form of a cosine function is \(y = a \text{cos}(bx + c) + d\), where:
  • \

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

Find the angular speed \(\omega\) for each of the following. a line from the center to the edge of a CD revolving 300 times per min

Over the interval \([0,2 \pi],\) compare the graphs of $$ y=\cos 3 x \quad \text { and } \quad y=3 \cos x $$ Can we say that, in general, \(\cos b x=b \cos x ?\) Explain.

Use the formula \(v=r \omega\) to find the value of the missing variable. $$r=8 \mathrm{cm}, \omega=\frac{9 \pi}{5} \text { radians per sec }$$

Suppose that point \(P\) is on a circle with radius \(r,\) and ray \(O P\) is rotating with angular speed \(\omega .\) For the given values of \(r, \omega,\) and \(t,\) find each of the following. (a) the angle generated by \(P\) in time \(t\) (b) the distance traveled by \(P\) along the circle in time \(t\) (c) the linear speed of \(P\) $$r=30 \mathrm{cm}, \omega=\frac{\pi}{10} \text { radian per } \sec , t=4 \mathrm{sec}$$

Work each problem. In a circle, a sector has an area of \(16 \mathrm{cm}^{2}\) and an arc length of \(6.0 \mathrm{cm}\). What is the measure of the central angle in degrees?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.