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Transforming Trigonometric Equation

  1. Apr 30, 2015 #1
    1. The problem statement, all variables and given/known data
    In 2001, Windsor, Ontario received its maximum amount of sunlight,
    15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on
    December 21
    1. Due to the earth's revolution about the sun, the hours of daylight function is periodic. Determine an equation that can model the hours of daylight function for Windsor, Ontario.
    2. Relevant equations
    y=a sin[b(x-c)] + d

    3. The attempt at a solution
    a=(max-min)/2=(15.28-9.08)/2=3.1

    b=2π/period=2π/365=0.02

    d=(max+min)/2=(15.28+9.08)/2=12.18

    To find , we must substitute y and x for 15.28 and 172, which is June 21, respectively.

    y=a sin⁡〖[b(x-c)]〗+d

    15.28=3.1 sin⁡〖[0.02(172-c)]〗+12.18

    15.28-12.18=3.1 sin⁡〖[170.28-0.99c]〗

    3.1=3.1 sin⁡〖[170.28-0.99c]〗

    1=sin⁡〖[3.44-0.02c]〗

    sin^(-1)⁡〖(1)〗=3.44-0.02c

    90=3.44-0.02c

    90-3.44=-0.02c

    86.56=-0.02c

    4328=c
     
  2. jcsd
  3. Apr 30, 2015 #2

    SammyS

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    Do you have a question?

    That's a huge round-off error for b.

    Plug in 355 & see what the answer is for that day.
     
  4. Apr 30, 2015 #3
    I am aware of the fact that the value I get for c is horribly skewed. I would like to know where exactly I have gone wrong.
     
  5. Apr 30, 2015 #4

    SammyS

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    The value of 0.2 for b is at least 16% larger than the correct value of 2π/365 . I think that's a significant error.

    How do you know that you've gone wrong?
     
    Last edited: Apr 30, 2015
  6. Apr 30, 2015 #5

    SammyS

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    Do you want to do this in degrees or in radians ?

    This appears to be the biggest issue. Using radians for b, then using degrees when evaluating the inverse sine will cause a BIG problem.
     
    Last edited: May 1, 2015
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