You should plot the daylight hours against the date to get a picture of the sine wave, to see how it looks. To find the values of the constants in y=D+A sin [B(t-c)], you can pick them off the plot (see below on how to do that).
The equation y=D+A sin [B(t-c)] is the general equation for a sine wave. Not all terms are used in all cases. So, first plot the sine wave on a chart, and from that you can discern the parameters for the sine equation.
Start by giving each date of the calendar a number from 0 to 364, from Jan 1 to Dec 31. Lets call this the day number.
Now, from the US Naval Observatory data, plot the hours of daylight against the day number for whatever data you have. You should get a sine-wave looking plot.
Now, lets figure out the equation parameters.
y=D+A sin [B(t-c)]
A = Amplitude, = peak-to-peak value / 2. Lets say that the maximum number of daylight hours is 14, and the minimum number of hours is 8. In this case, A = (14 - 8) / 2 = 3 hours. That is, both the positive and negative peaks of the sine wave will be 3 units away from the mean value of the wave.
D = offset. This is the average value of the sine wave. In the example above, D = (14 + 8) / 2 = 11 hours. The average value of sine wave ( y = sin(x) ) is zero. So, if your sine wave isn't centered about the x-axis, which it wont be in this case, because there's no such thing as negative daylight, the sinewave will have some average value. That is, there is some average value of sunlight across the year, with a maximum and minimum about that average, represented by the amplitude.
C represents the phase of the waveform. From the basic sine equation, y = sin(t), when t = 0, y = 0. That is, the value of the sine wave is right at its average value, with a rising slope. Now, for your equation, when t = 0 (date of Jan 1), the sine wave may not be at its average value. So, find a value of t (the date number) where the sine wave is at its average value and the slope is rising. Let's say that the average value occurs in April 1, so that the date number is 90 (90 days since the start of the year). This is the value that you'd use for C. All C is is an offset along the x-axis that shifts the equation left or right.
t is the date number. This is the input variable.
B is a scaling factor. The sin() function is periodic over a range of 2pi, which is a value of 6.28... But your input ranges from 0 to 364. So you need to scale it so that 0 maps to 0 and 364 maps to 2pi.
Set B = 2pi / 364
Since t ranges from 0 to 364, when you multiply B * t, you'll get a range from 0 to 2pi, which will give you one sine wave period across the full year.
Hope this helps,
-Guru