Chapter 4.2, Problem 82PE

Application Exercises

In Exercises 43-44, use a calculator in radian mode in parts (b) and (c).

The number of hours of daylight, H, on day t of any given year (on January $1,t=1$) in San Diego, California, can be modeled by the function

$H(t)=12+2.4\sin \left[\frac{2\pi }{365}(t-80)\right]$

a. March 21, the 80th day of the year, is the spring equinox. Find the number of hours of daylight in San Diego on this day.

b. June 21, the 172nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. Find, to the nearest tenth of an hour, the number of hours of daylight in San Diego on this day

c. December 21, the 355th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in San Diego on this day.