SOLUTION: The average monthly temperature of a town can be modeled by the function T(t)=14.6sin0.5(t-1)+9.15 where T is the temperature in degrees Celsius and t = 0 represents January 1, t =

Algebra ->  Trigonometry-basics -> SOLUTION: The average monthly temperature of a town can be modeled by the function T(t)=14.6sin0.5(t-1)+9.15 where T is the temperature in degrees Celsius and t = 0 represents January 1, t =      Log On


   

Question 1091295: The average monthly temperature of a town can be modeled by the function T(t)=14.6sin0.5(t-1)+9.15 where T is the temperature in degrees Celsius and t = 0 represents January 1, t = 1 represents February and so on. In which month is the average monthly temperature the highest?
a. March c. May
b. April d. June

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!

The 14.6 and 9.15 only affect the amplitude and the midline of the graph. The "sin(0.5(t-1))" is what determines what values of t give maximum, minimum, or average temperatures.

The sine function has its maximum value when the angle is pi/2. So
0.5%28t-1%29+=+pi%2F2
t-1+=+pi
t+=+pi+%2B+1

So the value of t that gives the maximum average temperature is pi+1, or about 4.14. Since t=0 represents January, 4 represents May. So the highest average monthly temperature is in May.