In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox. In this year, the equinox falls on March 21. In this task, you’ll use a trigonometric function to model the hours of daylight hours on certain days of the year in New York City.
1.Find the amplitude and the period of the function.
2.Create a trigonometric function that describes the hours of sunlight for each day of the year.
+37170 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:
+37170 Yes, slide backward from March 21st by 38 days to get to Feb 10th the read the 'y' value....or slide forward 328 days to Feb 10th,though you would really have to zoom in on the graph...
Use the equation 2.8833 sin (.9863(328)) + 12.133 = 10.42 hr = 10 hr 25 min
Here is a zoom-in of the graph:
