Elementary trigonometry based on a first order differential equation

2011/11/23 by Horia I. Petrache, Petrache, Horia I.
Mathematics · #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations #math.HO

paper · pdf · doi:10.48550/arxiv.1111.6839

5 pages

arxiv created 2011/11/23 · arxiv updated 2011/11/30

Abstract

It is shown that with appropriate boundary conditions, a real function satisfying the differential equation 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.

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