Rational values of powers of trigonometric functions
Genki Shibukawa
TL;DR
This paper extends classical theorems to identify when powers of trigonometric functions take rational values, broadening understanding of their algebraic properties.
Contribution
It generalizes previous results by Olmsted and Carlitz-Thomas to include powers of trigonometric functions, revealing new rationality conditions.
Findings
Extended theorems to powers of trig functions
Identified conditions for rational values of powers
Broadened algebraic understanding of trig functions
Abstract
We extend the theorem by Olmsted (1945) and Carlitz-Thomas (1963) on rational values of trigonometric functions to powers of trigonometric functions.
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Taxonomy
TopicsMathematical functions and polynomials · Functional Equations Stability Results · Iterative Methods for Nonlinear Equations