The given function is
[tex]f(t) = 33 sin( \frac{ \pi }{2} t) - 20[/tex]
with
t = time, hours
f = temperature, °C
Because the maximum and minimum values for the Sine function are +1 and -1 respectively,
The maximum value of f = 33 - 20 = 13.
The minimum value of f = -33 - 20 = -53.
The period, T, is given by
[tex] \frac{2 \pi }{T} = \frac{ \pi }{2} \\ \\ T=4[/tex]
Answer:
Maximum: 13°; Minimum: -53°; period: 4 hours
