/*! 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 110 Repeat Exercise 109 for data of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 110

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.

Short Answer

Expert verified
Create a sinusoidal function based on the average monthly temperatures using the formula \(y = A \sin(B(x - C)) + D\). Calculate A, B, C, and D using the data and check its effectiveness by comparing the predicted and actual temperatures.

Step by step solution

01

Understanding sinusoidal functions

A sinusoidal function can be represented by the formula \(y = A \sin(B(x - C)) + D\), where A is the amplitude (half the difference between maximum and minimum values), B determines the period (the total time for one complete cycle), C results in the horizontal shift (or phase shift) and D corresponds to the vertical shift (commonly the average value).
02

Identify data points

Collect the average monthly temperature data for a region of choosing. Consider that these temperatures vary in a periodic manner throughout the year.
03

Determine parameters for the sinusoidal function

The amplitude (A) would be half the difference between the highest and the lowest temperature. The period (B) would be the time it takes for a complete cycle to occur, which in case of month temperatures is 12. To find B, use the formula \(B = \frac{{2\pi}}{{\text{{period}}}}\). The phase shift (C) is the amount of horizontal shift, for it observe the month with the highest temperature, if it's July, for instance, a shift of 7 months will be necessary. The vertical shift (D), if necessary, is usually the average of the temperatures.
04

Construct the sinusoidal function

Substitute the parameters obtained from step 3 into the sinusoidal function formula.
05

Verify your function

Compare the temperatures predicted by your function to the actual temperatures. If there's a good match, it means the function accurately models the temperature trend.

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

Have you ever noticed that we use the vocabulary of angles in everyday speech? Here is an example: My opinion about art museums took a \(180^{\circ}\) turn after visiting the San Francisco Museum of Modern Art. Explain what this means. Then give another example of the vocabulary of angles in everyday use.

Determine the range of the following functions. Then give a viewing rectangle, or window, that shows two periods of the function's graph. a. \(f(x)=\sec \left(3 x+\frac{\pi}{2}\right)\) b. \(g(x)=3 \sec \pi\left(x+\frac{1}{2}\right)\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I made an error because the angle I drew in standard position exceeded a straight angle.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Using the equation \(y=A \sin B x,\) if I 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.

Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\frac{1}{2} \tan (\pi x+1)$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.