English

Elementary trigonometry based on a first order differential equation

History and Overview 2011-11-30 v1

Abstract

It is shown that with appropriate boundary conditions, a real function satisfying the differential equation f(x)=f(x+a)f'(x) = f(x+a) has all known properties of the sine function. A number of elementary derivations are presented including proofs for periodicity and trigonometric identities.

Keywords

Cite

@article{arxiv.1111.6839,
  title  = {Elementary trigonometry based on a first order differential equation},
  author = {Horia I. Petrache},
  journal= {arXiv preprint arXiv:1111.6839},
  year   = {2011}
}

Comments

5 pages

R2 v1 2026-06-21T19:43:18.893Z