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arXiv · 1111.6839

Elementary trigonometry based on a first order differential equation

Horia I. Petrache
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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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Horia I. Petrache. 2011-11-23. Elementary trigonometry based on a first order differential equation. https://arxiv.org/abs/1111.6839

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