Results 1 to 5 of 5
Like Tree2Thanks
  • 1 Post By HallsofIvy
  • 1 Post By skeeter

Thread: Need help with Hours of Daylight

  1. #1
    Newbie
    Joined
    Nov 2017
    From
    Canada
    Posts
    3

    Need help with Hours of Daylight

    For an assignment for school, Ihave to complete an assignment about hours of daylight.

    What I know is that the period is 365 days divided by 360 (=1.01), the amplitude is the lonest hours of daylight minus the shortest hours of daylight divided by 2. The midline is the longest hours of daylight plus the shortest hours of daylight divided by 2.

    However, I am not sure what the phase shift would be. Would it be 6, since hours of daylight change after 6 months?

    The function would look like this:
    2.675 sin [6(x-1.01)]+12.175
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,970
    Thanks
    3114

    Re: Need help with Hours of Daylight

    I am not sure what you mean by "the hours of daylight change after 6 months". The hours of day light change from day to day. Do you mean that, after 6 months, the hours of daylight stop increasing and start increasing? What does "x" represent here? Why are you subtracting 1.01? If that is to convert days to degrees, shouldn't you divide x by that? Also, asking about the phase shift, you suggest that "the hours of daylight change after 6 months". But the phase shift in the formula you give is NOT the "6" in the sine function but the "1.01" subtracted from x. As I asked before, what does "x" represent here? What values of x correspond to the least day light (winter solstice) and which the most (summer solstice). That is what affects the phase shift.
    Thanks from Erika5
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702

    Re: Need help with Hours of Daylight

    Little easier to use cosine ... $y(x)$ is hours of day light as a function of days in the year.

    $x=0$ is the start of the calendar year.

    $y=12.175-2.675\cos\left[\dfrac{2\pi}{365}(x+10) \right]$
    Attached Thumbnails Attached Thumbnails Need help with Hours of Daylight-ccb54f72-be7a-4254-9444-40a626122234.png  
    Thanks from Erika5
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2017
    From
    Canada
    Posts
    3

    Re: Need help with Hours of Daylight

    What I meant with 6 is that the hours of daylight stop increasing after 6 months and begin to decrease.

    The 1.01 is 360o divided by 365 days. For this assignment we were told that b is 360 divided by period. Now I realise that I misplaced it.

    The winter solstice would be 5.93 and the summer solstice would be 18.98.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702

    Re: Need help with Hours of Daylight

    The winter solstice would be 5.93 and the summer solstice would be 18.98.
    if those are the hours of daylight on Dec 21 (x = 355) and Jun 21 (x=172) ...

    $y = 12.455 - 6.525\cos\left[\dfrac{2\pi}{365}(x + 10)\right]$

    note the use of radians vice degrees in the function
    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. Sinusoidal formula for daylight hours
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: Apr 21st 2008, 01:23 PM

/mathhelpforum @mathhelpforum