Fourier Transform for triangular wave

Question

Could someone tell me if I've worked this out right? I'm unsure of the process, especially the final parts where I convert it to a sinc function.

Please let me know if I've made mistakes anywhere else too.

Answer 1

The mistake on the last step: $$ \frac{6}{\sqrt{2\pi}} \left[ \frac {\sin^2\frac{3\omega}2}{\frac{3\omega^2}2} \right] = \frac{6}{\sqrt{2\pi}} \left[ \frac {\sin^2\frac{3\omega}2}{\frac{2}{3}\left(\frac{3\omega}2\right)^2} \right] = \frac{9}{\sqrt{2\pi}} \left[ \frac {\sin\frac{3\omega}2}{\frac{3\omega}2} \right]^2 = \frac{9}{\sqrt{2\pi}} {{\rm sinc}^2\frac{3\omega}2} $$