# Write a sinusoidal function that models the number of daylight hours for the year in this city.

Words: 276
Pages: 2
Subject: Mathematics

Directions

Do a web search to find the sunrise and sunset times for the last year in the city in (or near) which you live. Print out the information you find.

Starting with January 1, calculate the number of daylight hours every 30 days. (You should have 13 items of data.) Convert the time from hours and minutes to the nearest tenth of an hour. For example, if the sunrise time is 0708, write the decimal 7.1, by dividing 8 by 60.

Graph this set of data on graph paper. The horizontal axis will represent the day of the year, and the vertical axis will represent the number of daylight hours. Be sure to title your graph and label the axis.

Draw a regression curve, a curve that best represents your set of data. (This is similar to drawing a line of best fit.)

Answer the following questions in the essay box below:

Locate the lowest and highest points on your graph. What is the amplitude?

There are 365 days in a year. Explain this value’s relationship to the graph.

What is the vertical shift of the graph?

What is the phase shift of the graph?

Write a sinusoidal function that models the number of daylight hours for the year in this city.

Using your equation, estimate the number of daylight hours in this city on the 220th day of the year. Based on your graph, does this answer seem reasonable? Explain any discrepancy that might occur between the two values.