Trig Cosine Word Problem (temperature of a chemical reaction oscillates between...)

[BigNate]

Problem: The temperature of a chemical reaction oscillates between a low of -12 degrees and a high of 12 degrees. The temperature is at its lowest point when t = 0 and completes one cycle over an 8 hour period.

Write a function of the chart and determine at what point during a 24 hr. day will the reaction first have a temperature of 8 degrees.

Here are my thoughts:
The function is a cosine function. It is something like f(t) = -12cos(___t). I just can't figure out how to fill in the blank and then figure out when the temp will be 8 degrees.

Can someone please help? Your help is greatly appreciated.

Thanks,
Nate

 

[mmm4444bot]

… one cycle over an 8 hour period.

… something like f(t) = -12cos(___t).

Another name for "one cycle" is "the period".

f(t) = A·cos(ω·t)

Amplitude = |A|

Period = 2·Pi/ω

To review this trigonometry, google keywords properties of sinusoidal functions.

Also, they ask, "at what point during a 24 hr day will the reaction first have a temperature of 8 degrees?" Did they tell you that t=0 corresponds to midnight? If not, then you can report only the number of hours elapsed since the first minimum temperature of the day (because we don't know when t=0 occured within the 24-hr day).