Question

The temperature of a chemical reaction ranges between -10°C and 50°C. The temperature is at its lowest point when t = 0 and completes one cycle over a six-hour period. What is a sine function that would model this reaction?

Answer 1

The range is 50 - (-10), so the amplitude will need to be 30, as sine goes from 1 to -1.

At t=0 to get the lowest point you will need sin = -1 thus at
- pi/2 or +3pi/2 when t = 0

If the period is 6 hours, then the time-varying argument of the sine function will be 2 pi t / 6 where t is in hours.

Put this together for your final answer.