Fourier Transform of sin(wt+phi)

[zanderace]

Homework Statement

I've been stuck on this for a while:

Find the Fourier transform of f(t)=sin([itex]\omega0[/itex]t+[itex]\phi[/itex])

Homework Equations

I know that I have to use F(ω)=[itex]\int[/itex]f(x)e^-iωt dt (between - and + infinity) to solve this

The Attempt at a Solution

So far I have: F(ω)=[itex]\int[/itex]Sin(ω0t+[itex]\phi[/itex])e^-i[itex]\omega[/itex]tdt
=[itex]\int[/itex](e^i[itex]\omega[/itex]0t+[itex]\phi[/itex] - e^-it[itex]\omega[/itex]0+[itex]\phi[/itex])/2i * e^-i[itex]\omega[/itex]t dt

(Both evaluated between - and +infinity, and ω0 means ω subscript 0)

But I'm really not sure where to go with this next. Any help or pointers would be really appreciated! Also sorry for my equation writing but I'm completely new to LATEX. Thank you.

 

[Dick]

The answer is going to involve a sum of Dirac delta functions. You might want to look up how the integral of a complex exponential is related to the Dirac delta.