First________________________ Last Name ________________________________________________________ Period ____ Daylight Hour Project -An Application of Cyclic Functions
Goal of the Project: To collect raw periodic data in the form of #of daylight hours over a year, in a city of your choice. Then create a cyclic function from that data. Step 1:
Collect and Record My Data . Use the website: http://aa.usno.navy.mil/data/docs/Dur_OneYear.php a)
b)
c)
d)
Select a city in the U.S. or any city in world. (pick a unique city from everyone else in the class). For the year 2015, create a table that shows the number of daylight hours by month/day. Record the number of hours/minutes for the 15th of each month. Record Below (example : Jan 15th is 09:57 ). Record below in row #3 Covert the hours (in hours:min) to just hours as a single decimal. This number will represent the # of Daylight Hours. . (For example: 08:41 would be 8.68 or 8.7 hours). If you can't figure out how to do this, "Google it" or use the help link on my website. (For example: 08:41 would be 8.68 or 8.7 hours) My City is _____________________________ Country ______________________________ Date Jan 15 Feb 15 Mar 15 April 15 May 15 June 15 July 15 Aug 15 Sept 15 Oct 15 Nov 15 Dec 15 day of Year 15 46 74 105 135 166 196 227 258 288 319 349 hrs:mins # of Daylight Hours (as a decimal) _____________________________________________________________________ continue on to back the back side. Step 2:
a) On a piece of graph paper, make a scatter plot of your 12 data points. The graph should be neat. Each axis should be labeled clearly. b) Data like this is periodic (or cyclic) so try to lightly draw a smooth sinusoidal curve through your points the best that you can. Your raw data should be clearly visible after your curve is drawn. c) Note: Sinusoidal does not mean sine or cosine. It just means that it is the same shape. d) Use a ruler to draw the midline. e) Label the midline with it's value somewhere on the graph. Do the same with the minimum and maximum daylight hours. f) Staple your graph below this paper when you are all finished. (with your name on both). Step 3:
Create a function that calculate the Number of Daylight Hours in your city vs. the Day of the Year Your equation should be in the form 𝐷(𝑡) = 𝑎 𝑠𝑖𝑛 [𝑏(𝑡 − ℎ)] + 𝑘 or 𝐷(𝑡) = 𝑎 𝑐𝑜𝑠 [𝑏(𝑡 − ℎ)] + 𝑘 Show your calculation for your b-­‐value (I would use degrees). b = My equation is: _____________________________________________________________________ (also write this equation on the blank line on the front side) Step 4:
Use your graphing calculator to check your equation's accuracy. Be sure to use degree mode. Try checking one or two data values that you collected and see if it is close. Remember this is not an exact model don't expect an exact match. Step 5:
My birthday is on __________________. What was the number of daylight hours on your birthday as predicted? ___________________ Optional Step 6:
For extra and amazing FUN, you can try to create a scatter plot on your GDC with your data and graph it simultaneously with your equation. Be sure to set up a window that matches the graph.