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Math Help - Laplace transform

  1. #1
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    Laplace transform

    Hi,

    I'm trying to find the laplace transform of the following function:

    f(t) = cos(at+b)

    I'm having trouble with eulers identity:

    I know exp(iat) = cos(at) + isin(at)
    I don't know if exp(iat+b) = cos(at+b) + isin(at+b)

    thx 4 help
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  2. #2
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    I calculated as if what I said earlier was true, I get:

    sexp(b) / (s^2+a^2)

    can anyone confirm? thx
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  3. #3
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    Quote Originally Posted by Provoke View Post
    Hi,

    I'm trying to find the laplace transform of the following function:

    f(t) = cos(at+b)

    I'm having trouble with eulers identity:

    I know exp(iat) = cos(at) + isin(at)
    I don't know if exp(iat+b) = cos(at+b) + isin(at+b)

    thx 4 help
    \cos (at + b) = \frac{1}{2} \left( e^{i(at + b)} + e^{-i(at + b)}\right).

    Quote Originally Posted by Provoke View Post
    I calculated as if what I said earlier was true, I get:

    sexp(b) / (s^2+a^2)

    can anyone confirm? thx
    This is not correct. The correct answer is  \frac{s \cos (b) - a \sin (b)}{s^2 + a^2}.
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