Results 1 to 2 of 2

Thread: daylight

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    4

    daylight

    in a given region, the number of daylight hours vaires, depending on the time of year. this variation can be approximated with a sinusoidal function. the model for a certain region is given by the function d(t)= 5sin 2pie/365 (t-95)+13, where d(t) is in hours and t represents the number of days after January 1. find two days whent he approximate number of daylight hours is 16h.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by anitha View Post
    in a given region, the number of daylight hours vaires, depending on the time of year. this variation can be approximated with a sinusoidal function. the model for a certain region is given by the function d(t)= 5sin 2pie/365 (t-95)+13, where d(t) is in hours and t represents the number of days after January 1. find two days whent he approximate number of daylight hours is 16h.
    $\displaystyle d(t)=5\sin\left(\frac{2\pi(t-95)}{365}\right)+13$

    The number of daylight hours you want is 16, so let d = 16...

    $\displaystyle 16=5\sin\left(\frac{2\pi(t-95)}{365}\right)+13$
    $\displaystyle 3=5\sin\left(\frac{2\pi(t-95)}{365}\right)$
    $\displaystyle \frac{3}{5}=\sin\left(\frac{2\pi(t-95)}{365}\right)$
    $\displaystyle \sin^{-1}(\frac{3}{5})=\frac{2\pi(t-95)}{365}$

    The value of $\displaystyle \theta$ for which $\displaystyle \sin \theta = \frac{3}{5}$ is $\displaystyle 0.643501$ and $\displaystyle \pi-0.643501=2.49809$

    $\displaystyle \{0.643501,2.49809\}=\frac{2\pi(t-95)}{365}$
    $\displaystyle \frac{365}{2\pi}\times\{0.643501,2.49809\}=t-95$
    $\displaystyle \{37.382,145.118\}=t-95$
    $\displaystyle \{132.382,240.118\}=t$

    So the amount of time is about 132 and 240 days after January 1 (respectively).

    Or the days are May 12 and August 28.
    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: Jun 14th 2011, 02:58 PM
  2. trig with hours of daylight, days after equinox
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Mar 13th 2011, 10:36 PM
  3. Minutes of Daylight Per Day
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Mar 7th 2010, 02:25 PM
  4. Sinusoidal formula for daylight hours
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: Apr 21st 2008, 01:23 PM

Search Tags


/mathhelpforum @mathhelpforum