Results 1 to 2 of 2

Math Help - Problem with sunlight hours trig equation

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    1

    Problem with sunlight hours trig equation

    Hi

    I have the equation s = -3.2cos(0.01726t + 0.15534) + 12

    s is equal to the number of hours of sunlight on a given day
    t is equal to the day number of the year

    If I am solving for t and s equals 13 hours I have tried to solve the equation like this

    13 = -3.2cos(0.01726t + 0.15534) + 12
    13 - 12 = -3.2cos0.01726(t + 9)
    1/-3.2cos0.01726 = t + 9
    -0.31 - 9 = t
    - 9.31 = t

    As I a have been told you take t and minus it from the mid point date which has the most number of day which is day 174 (as is explained in the question the lowest point in the year for sunlight is the 355th day) so that the two day when it is 13 hours of sunlight is 165th day and 183th day since it is a cos function and 13 hours falls on two different dates

    However according to my graph and other online info the days of the year for 13 hours of sunlight should be closer to the 97th day and 251st day of the year.

    I have been able to solve for s and the answer always works out correctly so the equation is correct. Why am I having trouble solving for t?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    1 = -3.2 \cos \left(0.01726(t + 9)\right)

    \cos \left(0.01726(t + 9)\right) = -\frac{1}{3.2}

    0.01726(t + 9) = \arccos \left(-\frac{1}{3.2}\right) or 0.01726(t + 9) = 2\pi-\arccos \left(-\frac{1}{3.2}\right)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving a Sinusoidal Equation for Hours of Daylight
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 14th 2011, 02:58 PM
  2. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 07:07 AM
  3. trig with hours of daylight, days after equinox
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 13th 2011, 10:36 PM
  4. yahtzee problem! due in 9 hours!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 30th 2006, 05:41 PM

Search Tags


/mathhelpforum @mathhelpforum