Here is a difficult one (for me at least): The number of min. of daylight per day, L(d), at 40 degrees north latitude is modeled by the function

L(d) = 167.5sin[(2pi/366)(d-80)] + 731

where "d" is the number of days after the beginning of 1996. (For Jan 1, 1996, d=1 and for Dec 31, 1996, d=366). What is the average number of minuates of daylight in 1996? (Out of common sense I would say, 12 hours, but I'm sure it's more complicated than that....)

Question

Here is a difficult one (for me at least): The number of min. of daylight per day, L(d), at 40 degrees north latitude is modeled by the function

L(d) = 167.5sin[(2pi/366)(d-80)] + 731

where "d" is the number of days after the beginning of 1996. (For Jan 1, 1996, d=1 and for Dec 31, 1996, d=366). What is the average number of minuates of daylight in 1996?  (Out of common sense I would say, 12 hours, but I'm sure it's more complicated than that....)

anonymous · Answer

The average value of A*sin(Bx+C)+D over one period is D, the trig function goes up (+A) and down (-A) equal amounts over one period. The 2pi/366 means one cycle over one year. So it averages 731 minutes per day over one year. Your presumption was close. 731/60=12.18333333