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Math Help - Y=ASin(bt+c)+D

  1. #1
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    Y=ASin(bt+c)+D

    The weather in Greens County in July is very regular. It varies from a low of 58 F at 4:00 AM to a high of 88 F at 4:00 PM. Find a formula that gives their temperature in terms of hours after 4:00 AM.

    I got Y=15sin(Pie/12t + c) + 73 so far.
    But how do I find c? What is c?
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    Quote Originally Posted by zweevu View Post
    The weather in Greens County in July is very regular. It varies from a low of 58 F at 4:00 AM to a high of 88 F at 4:00 PM. Find a formula that gives their temperature in terms of hours after 4:00 AM.

    I got Y=15sin(Pie/12t + c) + 73 so far.
    But how do I find c? What is c?

    c is going to depend on the starting value. If you choose midnight to be your starting value sub in point (t,Y) = (4:00AM,58) = (4,58) and solve for c.

    58=15sin(\frac{\pi}{12}(0) + c) + 73

    -15=15sin(\frac{\pi}{12}(0) + c)

    -1=sin(\frac{\pi}{12}(0) + c)

    c = \frac{2\pi}{3}
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