1. SIN function

I am having a little trouble with this problem. Any help would be greatly appreciated.

The daily consumption $C$ (in gallons) of diesel fuel on a farm is modeled by

$C=30.3+21.6sin(\frac{2PIt}{365}+10.9)$

(PI=3.14....)

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

so I know the $period=\frac{2PI}{\frac{2PIt}{365}}$ but then how do I simplify that?

b) What is the average daily fuel consumption? Which term of the model did you use? explain.

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

2. Originally Posted by OnMyWayToBeAMathProffesor
a)What is the period of the model? Is it what you expected? explain

so I know the $period=\frac{2PI}{\frac{2PIt}{365}}$ but then how do I simplify that?
Not Quite. Get the 't' out of there. You simplify it with algebra. How else?

$\frac{2\pi}{\frac{2\pi}{365}}$

2/2 = 1

$\frac{\pi}{\frac{\pi}{365}}$

$\frac{\pi}{\pi}\;=\;1$

$\frac{1}{\frac{1}{365}}$

Reciprocal and multiply

365

This better be ringing some bells.

3. Thank you very much, it now seems very obvious to me. and also thank you for reminding me what the latex code for $\pi$ is.

4. I also get 'c' but what about 'b'

5. The sine function has positives and negatives AROUND the average. These sine values cancel each other out when averaging over an entire cycle. This leaves only the constant term.

6. so the constant term in the equation is 30.3 correct?

7. Ding!!! All others in that expression are related to the sine.

Good call.

8. Thanks a lot

9. ...and, just for the record, on your way to your goal, you probably should learn how to spell "professor".

10. I had realized the misspelling after I had made username. But now I have firefox version 3, with spell check. Awesome browser, trumps all competition in security and features including add-ons. But google chrome seems to be coming up out of beta soon, so.... we will see what happens. Thanks again for you help.