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Math Help - SIN function

  1. #1
    Member OnMyWayToBeAMathProffesor's Avatar
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    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.

    I am confused on the rest, please help. Thank you.
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  2. #2
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    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.
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    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.
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  4. #4
    Member OnMyWayToBeAMathProffesor's Avatar
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    I also get 'c' but what about 'b'
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  5. #5
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    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.
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  6. #6
    Member OnMyWayToBeAMathProffesor's Avatar
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    so the constant term in the equation is 30.3 correct?
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  7. #7
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    Ding!!! All others in that expression are related to the sine.

    Good call.
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  8. #8
    Member OnMyWayToBeAMathProffesor's Avatar
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    Thanks a lot
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  9. #9
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    ...and, just for the record, on your way to your goal, you probably should learn how to spell "professor".
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  10. #10
    Member OnMyWayToBeAMathProffesor's Avatar
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    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.
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