Part B - Sinusoidal Function Analysis

You will now develop an equation and apply a sinusoidal function to model the number of hours of daylight. Search the internet to determine the number of hours of daylight at different times of the year at your home location. Either of these websites will be helpful: Daylight hours:

sunrise & sunset times throughout the seasons (weather2travel.com)or Sunrise and SunsetTimes Today | The Old Farmer's Almanac.

1.Record the data in the table below. Indicate your home location in the first line of the table.

Note: The number of hours must be given in decimal form. For example: A daylength of 9:40 means 9 hours and 40 minutes and would be expressed as 9.667 hours. Round all values to the nearest thousandth for this assignment.

Number of Daylight Hours at ___________________________________________
Date	Day Number (n)	Number of Daylight Hoursh(n)
January 1st	1	8
February 1st	32	5
March 1st	60	12
April 1st	91	14
May 1st	121	16
June 1st	152	16
July 1st	182	16
August 1st	213	14
September 1st	244	13
October 1st	274	11
November 1st	305	9
December 1st	335	8

1. Using theDesmos graphingcalculator,create table of values that represents the data in the table above.

1. Use an appropriate scale for each of the axes using the wrench icon in the top right corner of Desmos.

1. Use the sinusoidal regression on your graphing calculator to find a function, in the form h(n) = asin(bn + c) + d, that represents the hours of daylight, (), as a function of day number, , for your home location. Round the parameters to the nearest thousandth.

1. Now go back to your image in Desmos and enter the equation you found through the sinusoidal regression on your graphing calculator to verify that the function models the daylight data.

1. In the spaces below, identify the various characteristics of your sinusoidal function.

Sinusoidal Regression
Amplitude
Period
Equation of Midline
Domain
Range
Maximum
Minimum

1. Go back to your image in Desmos site that contains your sinusoidal information and enter the following second equation that models the daylight hours in Caracas, Venezuela: = 0.600 sin(0.520x 1.893) + 12.119.

1. Explain the similarities and differences in each of the three parameters (a, b, and d) in the two equations (your daylight function and the Caracas function). Do not just explain the differences in the values - what do these similarities and/or differences mean in the realworld context of the scenario?

1. In the space below, provide the graph or sketch of both functions. The functions must be on the same graph or sketch.

Appendix A - Desmos Graphing Software Directions

The Desmos graphing calculator website is a free graphing tool that offers a wide variety of graphing and other mathematical tools to users. Below is the link to the website and various support materials that will assist you in the development of your assignment.

Website:https://www.desmos.com/calculator

To Transfer Images to Desmos Grid:https://support.desmos.com/hc/enus/articles/203291245-Add-Image-to-Graph

To Plot Points:https://support.desmos.com/hc/en-us/articles/206902176-Plotting-Points

Creating a Table of Values:https://support.desmos.com/hc/en-us/articles/202529219-GettingStarted-with-Tables-of-Data

Creating a Regression:https://support.desmos.com/hc/en-us/articles/202532159-Regressions

To Export a Desmos Graph: https://support.desmos.com/hc/en-us/articles/202528789-ExportImage-of-Graph