Question

The temperature of a chemical reaction ranges between 30 degrees Celsius and 70 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 10-hour period. What is a cosine function that models this reaction?

Answer 1

Let us consider function as T= Acos(teta)+B, max and min values will occur when cos(teta) = +1 and -1;
so 30= -A+B;
70= A+B;
solving both B=50, A=20;
also at t=0 , cos(teta)= -1 and finishes one cycle after t=10hour;
so(teta) = pi+pi*t/10;
so, T= 20cos(pi+pi*t/10) + 50;