An elementary trigonometric equation
Victor H. Moll
TL;DR
This paper systematically investigates a class of trigonometric equations involving rational coefficients, highlighting special cases linked to classical results and exploring their algebraic properties.
Contribution
It introduces a systematic approach to analyze the equation A tan a + B sin b = C with rational parameters, including notable special cases.
Findings
Identifies conditions for solutions with rational coefficients.
Highlights a classical special case involving Pi/11.
Provides algebraic insights into the structure of solutions.
Abstract
A systematic study of the trigonometric equation A tan a + B sin b = C, where A, B and C^2 are rational numbers. The special case tan Pi/11 + 4 sin 3 Pi/11 = sqrt[11] appears in the classical literature.
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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematics and Applications