In 2020, on the summer solstice, June 20, Frederick, MD, experiences 15 hours and 2 minutes of daylight. Said differently, on the 171st day of the year, people on earth
at the latitude of Frederick experience about 15.0333 hours of daylight. On the
winter solstice, December 21, 2020, the same latitude has 9 hours and 29 minutes of
daylight; equivalently, on day 355, there are 9.4833 hours of daylight. This data is
essentially identical every year as the patterns of the earth's rotation repeat.
Let be the day of the year starting with = 0 on December 31, 2020. In addition,
let () be the number of hours of daylight on day in Frederick, MD. Find a formula
for a circular function () that fits this data. What is the function's midline,
amplitude, and period? What is the anchor point in your function?
Explain fully.