The temperature F in degrees farenheit for a summer day in M

The temperature (F in degrees farenheit) for a summer day in Massachusetts is given be F(t)=10cos(pi/12(t-7))+75, where t represents the time in hours, since 8:00am. Assume this model is only accurate for one day (0 t 24).

a. What is the average temperature for the day? Explain!!!!

b. What is the maximum temperature for the day? Explainn!!

I would like to see step by step so I understand :)

Solution

F(t)=10cos(pi/12(t-7))+75

maximum temerature is when cos(pi/12(t-7)) = 1

So, Fmax = 10 +75 = 85 F

miniumm temerature is when cos(pi/12(t-7)) = -1

Fmin = -10 +75 = 65 F

So, Average Temperature = (85 +65)/2 = 75 F