# Fourier Transform Question

## Homework Statement

Hi, I tried to work out the FT of cos(theta), and sin(theta + pi/2) which should both give the exact same FT since they are the same function.

However I get two different results as shown in the .jpg.

## Homework Equations

I used the 'time shifting' property to get that exponential in the second part.

## The Attempt at a Solution

#### Attachments

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vela
Staff Emeritus
Homework Helper
Multiply the exponential factor through and use the fact that $\delta(f-f_0) h(f) = \delta(f-f_0) h(f_0)$.

Multiply the exponential factor through and use the fact that $\delta(f-f_0) h(f) = \delta(f-f_0) h(f_0)$.
Thanks for your help! I never realised that.

I managed to work it out to almost the same as the cos function FT, however I am still left with the minus sign before the 2nd delta function, how do you get rid of that?

vela
Staff Emeritus