Fourier transform of sinusoidal functions

[asdf12312]

Homework Statement

Homework Equations

sinc(x) = \frac{sin(x)}{x}

The Attempt at a Solution

bit unsure how to get started?? i know transform of rectangular pulse pτ(t)=τ*sinc(τω/2∏)

also that sin(ωt)= e^jωt-e^-jωt / (2)

I could also probably sketch sinc(t/2∏), if that helps.

 

[asdf12312]

OK, so I guess I wasn't really thinking. There is duality property listed in my book, can I use that?

since x(t) ⇔ X(ω) then pτ(t)=τ*sinc(\frac{τω}{2\pi})

by duality X(t) ⇔ 2\pi*x(-ω) then τ*sinc(\frac{τt}{2\pi})=2\pipτ(ω)

so for a) it would be 2\pip1(ω). got this right at least? and how would i sketch this. would i be able to swap ω with t and just sketch the rectangular function p1(t) with amplitude 2\pi??