The amplitude will be 1/2 of the variance in day length 2 hrs 53 min x 1/2 = 1 hr 26 1/2 min
The period is 365 days (in a year)
Here is a graph (and the equation) with March 21st being the origin , x axis is days past March 21st and the y-axis is day length.
1.4416 is 1 hr 26 1/2 min in decimal .9863 is the degree value of each day(360 degrees in 365 days)
and 12.133 is the decimal equivalent of baseline equinox value of 12 hrs 8 miin
Note: I am not sure what 'vary by 2 hr 53 min from equinox' exactly means.....if it means the shortest day is 2 53 shorter and the longer day is 2hr 53 longer (which I now think it might) then the amplitude is 2 hr 53 = 2.8833 hr and the equation becomes
2.8833 (sin .9863x) + 12.133 and is shown here:
