The normal monthly high temperatures H (in degrees Fahrenheit) in Erie, Pennsylvania, are approximated by H(t) = 57.54 18.53 cos Ït / 6 - 14.03

The normal monthly high temperatures H (in degrees Fahrenheit) in Erie, Pennsylvania, are approximated by H(t) = 57.54 ˆ’ 18.53 cos Ï€t / 6 - 14.03 sin Ï€t / 6 and the normal monthly low temperatures L are approximated by L(t) = 42.03 ˆ’ 15.99 cos Ï€t / 6 - 14.32 sin Ï€t / 6 where t is the time (in months), with t = 1 corresponding to January (see figure).

(a) What is the period of each function?
(b) During what part of the year is the difference between the normal high and normal low temperatures greatest? When is it least?
(c) The sun is northernmost in the sky around June21, but the graph shows the warmest temperatures at a later date. Approximate the lag time of the temperatures relative to the position of the sun.

H(1) | L(1) + 4 3 ++ 6. 7. 9. 10 11 12 Month of year Temperature (in degrees Fahrenheit)