/*! 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 100 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 100

Use a graphing utility to graph \(y_{1}\) and \(y_{2}\) in the same viewing window. Use the graphs to determine whether \(y_{1}=y_{2}\) Explain your reasoning. $$y_{1}=\sin (x+4), \quad y_{2}=\sin x+\sin 4$$

Short Answer

Expert verified
Based on the plot and function analysis, \(y_{1}\) is not equal to \(y_{2}\). The first function is simply a shift of the sine function, whereas the second is a sine function fluctuating around a constant value of \(\sin 4\), and so the two are not the same.

Step by step solution

01

Plot the functions

In the graphing utility, the first function \(y_{1}=\sin (x+4)\) and the second function \(y_{2}=\sin x+\sin 4\) should be entered and then plotted. Both functions should be visible in the same viewing window to help in comparison.
02

Compare the plots

Next, visually examine both graphs. Look to see if their shape, location, and overall appearance match. If they do, this would suggest that \(y_{1}\) and \(y_{2}\) are the same.
03

Analyze function characteristics

Analyse the characteristics of the sine function in more detail. The first function is a horizontal shift of the sine function to the left by 4 units, whereas, the second function is the sum of two separate sine functions: a sine function and a constant function at \(\sin 4\). Summing up the functions in this way will not result in a smooth curve like the sine function, instead, it will show a fluctuation against a constant background value of \(\sin 4\).

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

Find the exact value of the expression. $$\frac{\tan 25^{\circ}+\tan 110^{\circ}}{1-\tan 25^{\circ} \tan 110^{\circ}}$4

Use the sum-to-product formulas to find the exact value of the expression. $$\sin \frac{5 \pi}{4}-\sin \frac{3 \pi}{4}$$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $$\sin 5 \theta \sin 3 \theta$$

Prove the identity. $$\sin \left(\frac{\pi}{2}-x\right)=\cos x$$

Use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. $$\tan ^{2} 2 x \cos ^{4} 2 x$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

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.