Laplace Transform for a trig function

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Try with that:

$$sin(2t)sin(5t)=\frac{1}{2}[cos(3t)-cos(7t)]$$

  • From: $sin(\alpha)sin(\beta)=\frac{1}{2}[cos(\alpha-\beta)-cos(\alpha+\beta)]$

  • After you can use this property: $\mathscr{L}[tf(t)]=-\frac{dF(s)}{ds}$

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abkds
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abkds

Updated on December 07, 2020

Comments

  • abkds
    abkds almost 3 years

    Help me finding the Laplace Transform using trig identities for: t sin(2t) sin(5t)

    this is what I've got so far:$\frac{1}{4i}[(s-7i)^{-2} + (s+7i)^{-2} - (s-3i)^{-2} - (s+3i)^{-2}]$ My Solution steps

    • FdT
      FdT almost 10 years
      Do you get $4i$ by the multiplication of $2i*2i$?
  • Ryan Reich
    Ryan Reich almost 10 years
    That's pretty much what they did, using complex exponentials.
  • FdT
    FdT almost 10 years
    @Ryan Reich: Sure, but, in this case you have to solve just $\mathscr{L}[tcos(t)]$ that you can solve immediately with the correlated property (I added it to the answer)