The number of hours of daylight that occur at any location on Earth depends on the time of year and the latitude of the location. The equations below model the numbers of hours of daylight in Seward, Alaska (60° latitude), and New Orleans, Louisiana (30° latitude).

In these models, D represents the number of hours of daylight and t represents the day, with t = 0 corresponding to January 1.
(a) Use a graphing utility to graph both models in the same viewing window. Use a viewing window of 0 ‰¤ t ‰¤ 365.
(b) Find the days of the year on which both cities receive the same amount of daylight.
(c) Which city has the greater variation in the number of hours of daylight? Which constant in each model would you use to determine the difference between the greatest and least numbers of hours of daylight?
(d) Determine the period of each model.

Transcribed Image Text:

T(t + 0.2) 182.6 D = 12.2 – 6.4 cos Seward D = 12.2 – 1.9 cos T(t + 0.2) New Orleans 182.6