# Thread: Need help with Hours of Daylight

1. ## 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

2. ## 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.

3. ## 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.

$y=12.175-2.675\cos\left[\dfrac{2\pi}{365}(x+10) \right]$

4. ## 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.

5. ## 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