Do I have to be affiliated with an institution to publish on arXiv? Is arXiv the right place to put it?
Independently of whether you need an affiliation, this sounds like a well-known representation of trig formulas (Euler's formula). There is quite some theory involved with this, including and up to Galois theory. You should check with someone knowledgeable whether you indeed discovered anything new. 

It's fun to discover new stuff, and it's a cool feeling to recover things that very smart people came up with, but, once you are there, you have to give it the reality check, which is the ultimate hallmark of the scientist.

Perhaps some friendly mathematician from the local college is happy to spare half an hour with a talented high schooler to give you at least an idea how novel the idea is or what else to try from this point on?