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Periodic Functions formula

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    The desert temperature, H, oscillates daily between 40 degrees F at 5 am, and 80 degrees F at 5 pm. Write a possible formula for H in terms of t, measured in hours from 5 am.


    3. The attempt at a solution
    The best I can come up with is

    H=60+40sin((pi/6)t)

    but this does not look right when I try and graph it on a calculator. I think the 40sin part is what I have wrong, but I cannot figure out what goes there, and the book is no help at all. Am I at least close?
     
  2. jcsd
  3. Feb 7, 2009 #2
    The amplitude of the oscillation is 40, but multiplying the base function by 40 will make it oscillate between -40 and 40, giving it an amplitude of 80. Ie., your function oscillates between 60 - 40 = 20 and 60 + 40 = 100.
     
  4. Feb 7, 2009 #3
    OK, I looked a little closer and I think they want it to start at 40. So I got H=60+(-20)cos((pi/12)t)

    I think I had the period wrong too... This looks right...right?
     
  5. Feb 7, 2009 #4
    Looks great!
     
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