# Thread: Problem with a Sin equation

1. ## Problem with a Sin equation

I had a problem with a question:

The daily consumption C (in gallons) of diesel fuel on a farm in modeled by
C= 30.3 +21.6sin[(2πt/365)+10.9]
where t is the time in days, with t=1 corresponding to January 1

A)What is the period of the model? Is it what you expected? Explain
B) What is the average daily fuel consumption? Which term of the model did you use? Explain?
C) Use a graphing utilty to graph the model. Use the graph to approximate the time of year when consumption exceeds 40 gallons per day

I have completely forgotten how to do sin functions and periods. I know this is probably a simple problem but I am having difficulty remembering how to do problems like this

2. The daily consumption C (in gallons) of diesel fuel on a farm in modeled by
C= 30.3 +21.6sin[(2πt/365)+10.9]
where t is the time in days, with t=1 corresponding to January 1

general form ...
$\displaystyle y = D + A\sin(Bt + C)$

A)What is the period of the model? Is it what you expected? Explain

period ... $\displaystyle T = \frac{2\pi}{B}$

B) What is the average daily fuel consumption? Which term of the model did you use? Explain?

note that the consumption will vary about the "D" value ... a max of D+A to a min of D-A

C) Use a graphing utilty to graph the model. Use the graph to approximate the time of year when consumption exceeds 40 gallons per day

graph the consumption equation and the line y = 40 ... you should be able to easily calculate the intersections.

3. For Period,
$\displaystyle \frac{2\pi}{k} =\frac{2\pi}{365}$

$\displaystyle Period\;k=365$

4. Thanks alot

5. I get A&C but could you possibly explain b more
if its max to min would it be D+A/D-A? which would be 51.9/8.7
but isn't it an average??

6. The normal way to get the average would be $\displaystyle \sum_{t=1}^{365}(30.3 +21.6\sin((2\pi t/365)+10.9))$. But skeeter was clever and knew from past experience that the average of this kind of function was halfway between the minimum and the maximum if you evaluated it at evenly spaced points over a whole number of periods. You could equally well know that the average of a function of the form

evaluated at evenly spaced points over a whole number of periods is $\displaystyle D$