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Math Help - periodic functions help!!

  1. #1
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    periodic functions help!!

    hi guys new here, looking for help and advice and here to help others.

    Currently studying maths in engineering

    Looking at a question as follows:

    Two are: 7sin vt and 5sin(vt + p/4)

    Use phasors and calculation to combine the two functions, expressing the result in Rsin (vt + alpha)

    This is what I have got

    y=7sin vt
    y=5sin (vt + p/4)
    y=7sin vt + 5sin (vt + p/4)
    y=Rsin (vt+a)

    co sine rule:

    a squared = b squared + c Squared 2b.cosA

    a squared = 5 squared + 7 squared 2 x 5 x 7 0.707

    a squared = 74

    Am I on the right lines, I am using an example did previus but cant work out where the 0.707 comes from

    Help in doing this be great
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  2. #2
    MHF Contributor
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    You can see the formula on this Wikipedia page (starting with "More generally..."). In those notations, a = 7, b = 5 and \alpha=\pi/4. The number 0.707=\sin\alpha=\cos\alpha. In my calculations, c\approx11.113 and \beta\approx0.324, so the answer is c\sin(vt+\beta) (this needs double-checking).
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