Finding a minimum value of an expression I have this question to solve:
A city's temperature of y degrees Celsius on a day in February is given by $y = 16 + 8 \sin \left(\dfrac{\pi t}{12}\right)$ where t is the time in hours after 9am.
a). What is the minimum temperature?
b). At what time is the temperature a minimum?
c). What is the temperature at 5pm?
Any help would be appreciated. Thanks.

(b) $0=y'=\frac{2\pi}{3}\cos\left(\frac{\pi t}{12}\right) \Rightarrow t=6 \Rightarrow$ The time at which the temperature is minimal is $3$pm.
(a) In $t=6$, the temperature is minimal. So the minimum temperature is 24 degrees Celsius.
(c) The temperature at 5pm is calculated in $t=8$, ie, $y(8)=16+4\sqrt{3}$.
