Laplace Transform f(t) = e^t *sin(t)sin(5t)

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To perform the Laplace Transform of the function f(t) = e^t * sin(t)sin(5t), the addition formula for sine can be applied. This formula states that sin(t)sin(5t) can be rewritten as (cos(4t) - cos(6t))/2. By substituting this expression into the original function, the transformation can be simplified. The resulting function can then be transformed using standard Laplace Transform techniques. This method allows for the successful application of the Laplace Transform to the given function.
tim_3491
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Hey everyone

Does anyone know how to do the following Laplace Transformation

f(t) = e^t *sin(t)sin(5t)

i can do it with one sin function but don't know how to do it with 2.

any help would be appreciated.
 
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tim_3491 said:
Hey everyone

Does anyone know how to do the following Laplace Transformation

f(t) = e^t *sin(t)sin(5t)

i can do it with one sin function but don't know how to do it with 2.

any help would be appreciated.

Use the addition formula for sines:

sin(t)sin(5t) = (cos(4t) - cos(6t))/2
 
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