..... 80 H(t) 60 40 L(t) 20 ********** * ++++++++ +i 2 3 4 5 6 8 9 10 11 12 Month of year Temperature (in degrees Fahrenheit)
Meteorology The normal monthly high
temperatures H (in degrees Fahrenheit) in Erie,
Pennsylvania, are approximated by
H(t) = 57.54 − 18.53 cos πt
6 − 14.03 sin πt
6
and the normal monthly low temperatures L are
approximated by
L(t) = 42.03 − 15.99 cos πt
6 − 14.32 sin πt
6
where t is the time (in months), with t = 1 corresponding
to January (see figure). (Source: NOAA)
1 2 3 4 5 6 7 8 9 10 11 12
20
40
60
80
Month of year
Temperature
(in degrees Fahrenheit)
t
L(t)
H(t)
(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 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.
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