Can the Dirac Delta Function be Used to Find the Fourier Transform of sin(at)?

[Jncik]

Homework Statement

find the Fourier transform of sin(at)

Homework Equations

The Attempt at a Solution

I'm not sure about the solution but

it is known that

now I tried using the formula of Fourier transform but I couldn't find anything

my question is this:

can I use the definition of the dirac delta function in order to find it?

If I remember correctly we have

[URL]http://latex.codecogs.com/gif.latex?e^{i\omega_{0}%20t}%20%3C-%3E%202\pi%20\delta%20%28\omega%20-%20\omega_{0}%29[/URL]

hence the result would be

i π δ(ω+α) - i π δ(ω-α)

is this correct?

 

[jbunniii]

Yes, it's correct.

 

[Clever-Name]

looks right to me. sin(at) is one of the functions that is listed in tables in any textbook with Fourier transforms so it would be easy to check your answer.

 

[Jncik]

thanks for your help :)