Elementary trigonometry based on a first order differential equation

Details Elementary trigonometry based on a first order differential equation Elementary trigonometry based on a first order differential equation

2011-11-23

arxiv.org/abs/1111.6839v1

Mathematics

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5 pages

Scientific paper

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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