Meteorology The normal monthly high temperatures H (in degrees Fahrenheit) in Eric, Pennsy...

Meteorology The normal monthly high temperatures H (in degrees Fahrenheit) in Eric, Pennsylvania, are approximated by

H(t) = 56.94 − 20.86 cos − 11.58 sin

and the normal monthly low temperatures L are approximated by

L(t) = 41.80 − 17.13 cos − 13.39 sin

where tis the time (in months), with t =1 corresponding to January (see figure). (Source: National Climatic Data Center)

(a) What is the period of each function?

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

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(c) The sun is northernmost in the sky around June 21, 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.