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October 25th, 2015, 07:47 AM  #1 
Newbie Joined: Oct 2015 From: NY Posts: 1 Thanks: 0  Calculus Modeling FormulasSeasons and Months
The following formula is a mathematical model for the number of hours of daylight on the t day of the year: L(t)=12+2.9sin[2pi/3659(t80)] 1. Use this model to compare how the number of hours of daylight is increasing from a) March 21stJune 21st b) June 21stSept 21st c) Sept 21stDec 21st d) Dec 21stMarch 21st 2. Use this model to compare how the number of daylight is increasing from a) Jan 6thFeb 6th b) Feb 6thMar 6th and so on.... During which time period is the amount of light increasing the most? What is the significance of "12", "2.9 (0 being the equator and 12 being the North Pole), "2pi", "2pi/365", "80", and "t80" in the model formula? THANKS SO MUCH!!! EVEN AN EXPLANATION ON HOW TO DO IT AND DOING ONLY THE FIRST FOR EACH WILL BE A REALLY BIG HELP. 
October 26th, 2015, 02:49 PM  #2  
Senior Member Joined: Jul 2012 From: DFW Area Posts: 635 Thanks: 96 Math Focus: Electrical Engineering Applications 
Hi Nzerb, and welcome to the forum. I assume that you meant: $\displaystyle L(t)=12+2.9 \sin \left(\frac{2\pi}{365} \cdot (t80) \right)$ Quote:
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At higher latitudes the number will be higher, tending to a very large number for the North Pole, with numbers greater than 24 truncated to 24 and numbers less than 0 truncated to 0. With the coefficient of the sine term at 0 for the equator, can you see the significance of the 12? Since the sine function repeats every $2\pi$ units and a year is roughly 365 days long, can you see the significance of the $2\pi$ and $\large \frac{2\pi}{365}$ terms? To see the significance of the 80 and the t80, consider when the number of hours of sunlight is a minimum, on the day of the winter solstice. When is the sine function a minimum? When is the winter solstice for the northern hemisphere? Does this help? Note: The t values for the dates are given here.  

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