fourier series / fourier series transform

Question

Find the trigonometric Fourier of the triangular waveform shown over the interval (-π, π) .

Answer 1

You should always add a description of what you‘ve tried so far to answer the question yourself. But since this is your first post on this site, I‘ll try to help anyway:

The trigonometric Fourier series is given by:

f(x) = $a_0 + \sum_{n=1}^\infty a_ncos(\frac{2\pi n x}{L}) + b_nsin(\frac{2\pi n x}{L}) $

With $a_0 = \frac{1}{L}\int_0^L f(x) dx$, $ \ \ a_n = \frac{2}{L}\int_0^L f(x) cos(\frac{2\pi n x}{L}) dx$, $\ \ b_n = \frac{2}{L}\int_0^L f(x) sin(\frac{2\pi n x}{L}) dx$

Where $L$ is f‘s period (in your case $2\pi$).

Since your function is even and has an average value of $0$ over one period, you only need to calculate the $a_n$.