James teacher has asked him to create a mathematical model for the temperatures for a cloudless and windless day in February. He has been told that the lowest temperature was 7 celcius at 3am and the highest temperature was 29 Celcius at 3pm. James decides to use trigonometric model for the temperature.
Determine a trigonometric models the given data from midnight(at the start of the day)to midnight(at the start of the next day) ie. over the 24hr period of the day.

Question

noelgreco · Answer

$$y=Asin(Bx+C)+D$$

Figure out A,B,C,and D one at a time.

A is the amplitude, which is 1/2 the distance between the extreme y-values.

B relates to the period, you already know that the period is 24.
$$B=\frac{Period}{ 2\pi }$$