I’m trying to make a complex sine wave by adding multiple instances of the same function with different values as a list, but I don’t know how to add those instances together.

I don’t know if this is the simplest way but you can use:
\sum_{n=1}^{\operatorname{count}\left(f\left(x\right)\right)}f\left(x\right)\left[n\right]
I doubt this is the best way though.

I think this would work in graph world. This allows for a dynamic list of elements (i.e 5 to 5 bajillion different transformations) and will randomly generate for you. https://www.desmos.com/calculator/wqgczw3hwv