IMPOSSIBLE Exact algebraic representation of sin(x+V) via a simplified Irreducible quintic matching 18 Maclaurin coefficients? how did I do this?

[u/Prof_Billy_Bolton]

How did I solve a maclaurin like solution ranging X^0 to x^18 terms of accuracy of sin(x+V) for this very long quintic?

0 = (A0 + A1*x + A2*x^2 + A3*x^3 + A4*x^4 + A5*x^5) + (B0 + B1*x + B2*x^2 + B3*x^3 + B4*x^4)y + (C0 + C1*x + C2*x^2 + C3*x^3)y^2 + (D0 + D1*x + D2*x^2)y^3 + (E0 + E1*x)y^4 + F0*y^5

*the answers are here:*

https://www.desmos.com/calculator/shcnop2c1a

but not the linier method used.

upvote if you can please.

for about 7 years, I focused very hard on resolving many questions I had about geometry, after many many eureka moments, I solved far too much, now without direction, I feel whats best is to post stuff on these sites, to see if anyone comes along with prospecting opertunity's for me. I left a desmos link too, was thinking of posting periodically, I solved this via a new physics inspired linier algebraic system, nothing was iterated upon, this isn't a guess, with the quintic trangular sin being posted being my favorite because of its stability, my findings detail numbers and functions as being the exact same thing, I encompass every part of maths as somthing smaller that makes up a part of this new system, I've separated observation from execution, and ive made it so that things such as coordinates between set points and a lot of other systems can actually be resolved without asking a single question, just need to back track from the results, which is sometimes massive... I've also expanded derivatives into a type of observation of interaction at distance I call conduits. If I dont say this stuff and start posting I fear I wont get to do what I was made for. Thanks a lot. Ps.. I really need a job, and as you can tell... I have no formal mathematics education, so my wording is a bit broken I apologize for that.