**Average Monthly Temperature Data**This table shows the average monthly temperatures in degrees Fahrenheit, collected by the U.S. National Oceanic and Atmospheric Administration.| Month, x | Average Monthly Temperature, °F ||-----------|----------------------------------|| January, 1 | 36.0 || February, 2 | 39.0 || March, 3 | 46.8 || April, 4 | 56.8 || May, 5 | 66.0 || June, 6 | 75.2 || July, 7 | 79.8 || August, 8 | 78.1 || September, 9 | 71.0 || October, 10 | 59.5 || November, 11 | 49.6 || December, 12 | 39.7 |**Source:** U.S. National Oceanic and Atmospheric Administration**Explanation:**The data illustrates the change in average temperatures throughout the year, starting from January to December. The temperatures range from a low of 36.0°F in January to a high of 79.8°F in July. This data can be used to study seasonal variations in temperature and understand climatic patterns. **Monthly Temperature**The data below represent the average monthly temperatures for Washington, D.C.(a) Draw a scatter diagram of the data for one period.(b) Find a sinusoidal function of the form $ y = A \sin (\omega x - \phi) + B $ that models the data.(c) Draw the sinusoidal function found in part (b) on the scatter diagram.(d) Use a graphing utility to find the sinusoidal function of best fit.(e) Graph the sinusoidal function of best fit on a scatter diagram of the data.---**Instructions for Educators:**- Begin by introducing the concept of sinusoidal functions and how they can be used to model periodic data.- Use the steps to guide students through creating a scatter plot and fitting a sinusoidal function to given temperature data.- Encourage the use of graphing utilities or software for accurate plotting and analysis.- Discuss the significance of parameters $A$, $\omega$, $\phi$, and $B$ in shaping the graph of the sinusoidal function.- Engage students in discussions about the accuracy and application of sinusoidal models in real-world scenarios.

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Answered: Average Monthly Temperature, F Month, x…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Average Monthly Temperature, F Month, x January, 1 36.0 February, 2 39.0 March, 3 46.8 April, 4 56.8 May, 5 66.0 June, 6 75.2 July, 7 79.8 August, 8 78.1 September, 9 71.0 October, 10 59.5 November, 11 49.6 December, 12 39.7 Source: U.S. National Oceanic and Atmospheric Administration