A completeness theorem for trigonometric identities and various results on exponential functions

van den Dries, Lou

doi:10.1090/S0002-9939-1986-0818470-6

A completeness theorem for trigonometric identities and various results on exponential functions
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by Lou van den Dries

Proc. Amer. Math. Soc. 96 (1986), 345-352

DOI: https://doi.org/10.1090/S0002-9939-1986-0818470-6

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Abstract:

All valid identities in terms of variables, real constants, the arithmetic operations of addition and multiplication, and the trigonometric operations of sine and cosine are shown to be consequences of a few familiar identities and numerical facts. We also indicate how to decide whether $f$ eventually dominates $g$, for $f$ and $g$ from a certain class of exponential functions. Finally, we correct a statement from an earlier paper.

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