# Fourier transform of sin

## Homework Statement

Hey guys.
I need to find the Fourier transform of sin, is this right?

http://img156.imageshack.us/img156/5531/scan0004r.jpg [Broken]

I searched the internet but all I could find is the answer with the dirac delta and I don't need that.

Thanks.

## The Attempt at a Solution

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## Answers and Replies

dx
Homework Helper
Gold Member
The Fourier transform of sin(t) involves the Dirac delta function. What do you mean by "I don't need that"? And why did you change the limits from -∞ to ∞ to -π to π in your integral?

The Fourier transform of sin(t) involves the Dirac delta function. What do you mean by "I don't need that"? And why did you change the limits from -∞ to ∞ to -π to π in your integral?

Oh, sorry, I need to find it from -pi to pi.
Is there something wrong with what I did?

Thanks.

dx
Homework Helper
Gold Member
I didn't read your whole solution, but there is a mistake in your first step. The Fourier transform integral goes from -∞ to ∞. Why did you change those limits?

I didn't read your whole solution, but there is a mistake in your first step. The Fourier transform integral goes from -∞ to ∞. Why did you change those limits?

Yeah, I need to find it from -pi to pi.
Is that way it doesn't involves Dirac function?

Thanks.

dx
Homework Helper
Gold Member
No! It's not from -pi to pi. It's -∞ to ∞.

No! It's not from -pi to pi. It's -∞ to ∞. But that is the question.
Find Fourier transform of sin in -pi<t<pi.

What do you mean?

Thanks.

Cyosis
Homework Helper
Your question is to transform the function $$f(t) = \left\{ \begin{matrix} \sin t & \mathrm{if}\; -\pi < t < \pi \\ 0 & \mathrm{otherwise} \end{matrix} \right$$ ?

Your question is to transform the function $$f(t) = \left\{ \begin{matrix} \sin t & \mathrm{if} -\pi < t < \pi \\ 0 & \mathrm{otherwise} \end{matrix} \right$$ ?

Yeah, sorry for the misconfusion.

Cyosis
Homework Helper
Then your approach is correct since the function is zero outside -pi<t<pi anyway so you may as well integrate from -pi to pi.

dx
Homework Helper
Gold Member
Ah, now it makes sense! Thanks Cyosis!

Cyosis
Homework Helper
You're welcome.