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Math Help - Finding trig function of given graph

  1. #1
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    Finding trig function of given graph

    So, one question i'm stuck in is "Find a formula for the graph of the function y=f(x) given in the figure above." (below)

    Finding trig function of given graph-obread-1874-sethomework5prob3image1-2-.png

    For the formula f(t) = Acos(B(t+h))+C, I figured the following out:

    amplitude = 3
    period = 2π (2π/B=2π, B=1)
    h (horizontal shift) =
    π
    C (vertical shift) = 4

    and replaced into the formula to get:

    f(t) = 3cos(1(t+π))+4

    Now when I graph that on my calculator, it looks fine, but it's not the correct answer. Where did I mess up? Am I even supposed to be using cos? The only reason I did is because it seemed like calculating h (the horizontal shift) would be easier for cos than sin, but I don't see why it shouldn't work either way.

    Any help is greatly appreciated.
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  2. #2
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    Re: Finding trig function of given graph

    First of all, it should be obvious that your A value is negative. Why?
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  3. #3
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    Re: Finding trig function of given graph

    Quote Originally Posted by Prove It View Post
    First of all, it should be obvious that your A value is negative. Why?
    I thought my A value was half the distance between by max and min Y values, so 7-1 = 6, 6/2 = +3 ? Unless i'm supposed to do it the other way round (-3)??

    Or do you mean that rather than a shift, my graph is flipped around? So something like C-Acos(B(t+h)) ?
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  4. #4
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    Re: Finding trig function of given graph

    Yep. That was it. I plugged the values into C-Acos(B(t+h)) and I got 4-3cos(x), which was correct.

    Thanks a ton for the help, I didn't even realize that my graph was a flipped cosine. However, for future reference, would it have also been right to see it as having shifted left/right by π like so: 4+3cos(x+/-π) ? In class, we were told to account for the difference that way, and it seems like that would be more universally applicable.
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