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Precalculus bonus project

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									Pre-Calculus Project – Let the Sun Sine!                    Name____________________

Introduction
Why study sine functions? We know by now that the graph of a sine function is a wave.
Did you know that many things in science and nature have graphs that look like a sine wave?
Functions whose graphs look like a sine wave are called sinusoidal functions. In this
project you will learn some applications of sinusoidal functions. You will also be using a
sinusoidal function to represent a real life situation. In particular, you will be using a sine
function to represent the number of daylight hours that occur per day for a city of your
choice. Before you begin, click on the links below and answer the questions.

1. List 5 applications of sinusoidal functions. Click Here for some examples. Research
others on your own.




2. A sinusoidal function can be used to represent anything that follows a cyclic pattern.
Read about the summer and winter solstices and describe how this relates to a sinusoidal
function.




Activity
Step One: Complete the worksheet Pre-Calculus Activity – Fitting Data to a Sinusoidal
Function and attach

Step Two: Choose a city anywhere in the world. Ok, almost anywhere. We don't want to
choose a location in the Artic and Antarctic regions. Read here and explain why a location
in these regions would not be well represented by a sinusoidal function.




Your city __________________________
Step Three: Find the date of the summer and winter solstice for any year on this chart.
Determine the day of the year that this date corresponds to. For example, the summer
solstice of 2001 occurred on June 21st, the 172nd day of the year. Be careful about leap
years and remember if you choose a location in the Southern Hemisphere the summer and
winter solstices are reversed.
Date of Summer Solstice____________ (mo/day/yr) Day of year_________________
Date of Winter Solstice____________ (mo/day/yr) Day of year_________________

Step Four: Find the number of daylight hours that occurred on the solstices for your city
and your year by clicking on the links below.
Cities in the U.S. and Canada
International Cities (on this link you create a calendar that shows you sunrise and sunset
times for month and year but the cities choices are limited)

Convert the number of daylight hours to a decimal by dividing the minutes by 60.

No. of daylight hours on summer solstice_________________
No. of daylight hours on winter solstice_________________

Step Five: Use the data above to write the sinusoidal function of the form
y = a sin (bx – c) + d that represents the number of daylight hours for your city and year.
Use the function to predict the number of daylight hours for April 17th, 2010.

Your function________________________
No. of daylight hours on April 17th, 2010 ____________

Step Six: Graph your function by hand or using this grapher and attach.



Project Rubric – due Feb 26th, 2010
Introduction: 5 points
Step One: 5 points
Step Two: 5 points
Step Three: 5 points
Step Four: 5 points
Step Five: 15 points
Step Six: 10 points
Total: 50 points

								
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