The average monthly temperatures for the middle of each month for New Orleans are plotted. Showing all of your work, write an equation of the average daily temperature graph.

Question

The points on the graph are (15, 12), (105, 20), (197, 28). I used the maximum and minimum points to find the amplitude and vertical shift. I am struggling to find the c value of y=asin(bx-c)+d. Also, I am writing a sine function.

Amplitude=(28-12)/2=8

D:y=(28+12)/2=20

Period=365

B=2π/P=2π/365

Answer 1

To calculate C you can use the point (105, 20).

Conveniently, its y-value is 20, i.e., same as D.

That means that

sin(105B - C) = 0

105B - C = 0

C = 105B = 105 x 2π/365 = 1.8