4. Based on years of weather data, the expected low temperature T (in oF) in Fairbanks, Alaska, can be
approximated by
T = 36 sin
?
?
?
?
?
?
2?
365
(t ? 101)
?
?
?
?
?
?
+ 14,
where t is in days and t = 0 corresponds to January 1.
(a) Find the amplitude, the period, and the phase shift. Then sketch the graph of T for 0 ? t ? 365.
(b) Predict when the coldest day of the year will occur.