Modeling with periodic functions

Question

In the month of March, the temperature at the South Pole varies over the day in a periodic way that can be modeled approximately by a trigonometric function.
The highest temperature is about $−50​$℃, and it is reached around $2$ p.m. The lowest temperature is about $−54​$℃ and it is reached half a day apart from the highest temperature at $2$ a.m.
Find the formula of the trigonometric function that models the temperature $T$ at the South Pole in March $t$ hours since $2$ p.m. Define the function using radians.
The trig function for $T$=$2\cos(\frac{πt}{12})-52$
so my Question is at $2$ pm and at $2$ am temperature is high $−50​$℃ as given in question but when i plot the graph for the function T=$2\cos(\frac{πt}{12})-52$
i get temperature at $2$ am the lowest i.e $−54​$℃ why is it so?

Answer 1

You are measuring time in hours from 2pm. So 2am corresponds to $t=12$, and so your temperature is: $$ T=2\cos(\pi)-52=-54 $$ Which is correct. The temperature is at a maximum of $-50$ at 2pm and a minimum of $-54$ at 2am. Which is what the question is trying to say. The wording though is slightly confusing and you might be reading it as saying that it is a maximum at 2am?