The longest day of year in Las Cruces is approximately 14 hours and shortest is ten hours of daylight. Graph of length of day over entire year is the sinusoidal function.
a) Determine the function which models number of hours of daylight t days after January 1. Suppose that year has 365 days and that spring equinox, when day is 12 hours long, is on 80th day of year. Also graph function. The function is at its midline on 80th day of the year.
b) Find on which days daylight lasts for accurately 13 hours.