A cubic formula that you probably haven't seen before!

I just learned this cubic formula with cosine from Wikipedia. The idea is to solve the depressed cubic equation x^3+px+q=0 with the triple angle identity of cosine. However, I don't think this formula is any useful. But is it cool? YES! How to depress a general cubic polynomial ax^3+bx^2+cx+d https://youtu.be/ULsPhWmqhyc?si=GhAQTzUXV1vmu15P&t=545 The cos(3x) identity: https://youtu.be/ONKPlyN1hpo?si=rP3Ykm18YAnNho0l Cubic Equations on Wikipedia: https://en.wikipedia.org/wiki/Cubic_equation 0:00 Solve x^3-28x+48=0 4:36 The proof ---------------------------------------- Big thanks to my Patrons for the full-marathon support! Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet Ö An R Camila L Luupo Farrah Batman 1127 Mathguru Дмитрий П. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D. 💪 Support this channel and get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 ---------------------------------------- #blackpenredpen #math #cubicequation