So I was playing with desmos and I was entering a random sum of sines and cosines and I noticed I had a weird shape forming.
So compactly written, what I was basically noticing was $\displaystyle \lim_{k \to \infty} \sum_{n=0}^{k}\frac{\sin((2n+1)x}{2n+1}$ was a rectangle thingy.
And then when I put a $(-1)^n$ and squared the denominator, it turned into a triangle!
So lets say I have a random function. And lets say I want to splice the portion from $(0,2π)$ and turn that into a periodic function. Is there some way to do that??? And it would have to be only sine and cosine because they are repeating.