Laplace transform of sin(4t+5)

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The discussion focuses on finding the Laplace transform of sin(4t+5) using trigonometric identities. The user applies the identity sin(a+b) to express sin(4t+5) as sin(4t)cos(5) + cos(4t)sin(5) before attempting the transform. There is uncertainty about the correctness of the result, prompting a request for alternative verification methods. Another participant suggests directly integrating sin(4t+5) multiplied by exp(-st) from 0 to infinity as a means to confirm the answer. The conversation emphasizes the importance of verifying results in mathematical transformations.
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Homework Statement



get laplace transform of sin(4t+5)


Homework Equations


using some trig identity i.e. Sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
or any other that could simplify it

The Attempt at a Solution


applying the trig identity
=sin(4t)cos(5)+cos(4t)sin(5)
taking the transform :
4cos(5)\frac {1}{s^2+16} +s*sin(5)\frac{1}{s^2+16}
why do i not trust this result, can anyone point me in the right direction?
 
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Why don't you trust it? It looks fine to me.
 
It might be right but i would like an alternative method to confirm the answer i got
 
You could compute it directly. Integrate sin(4t+5)*exp(-st) from t=0 to t=infinity. You'll get the same thing.
 

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