Question

For the 18-hour time period beginning at midnight, the temperature F in a particular room is given by the function F(t) = -12sin(t/3) + 78, where t is measured in hours

Answer 1

During which two consecutive hours does the temperature reach a maximum?

Answer 2

Please, note that the maximum of your function F(t) is at t=9 pi/2.
I used the Mathematical Analysis theorems

Answer 3

and F(9 pi/2)=12+78=90