Chapter 8.3, Problem 84E

HOW DO YOU SEE IT? The normal monthly high temperatures for Erie, Pennsylvania, are approximated by

$H\left(t\right)=56.72+23.62\text{ sin}\left(0.50t-2.08\right)$ and the normal monthly low temperatures for Erie, Pennsylvania, are approximated by

$L\left(t\right)=41.89+21.52\text{ sin}\left(0.52t-2.27\right)$ where t is the time (in months), with t = 1 corresponding to January. (Source: National Climatic Data Center)

(a) During what part of the year is the difference between the normal high and low temperatures greatest? When is it least?

(b) The sun is the farthest north in the sky around June 21, but the graph shows the highest temperatures at a later date. Approximate the lag time of the temperatures relative to the position of the sun.