TL;DR
This paper derives algebraic expressions for sums of powers of sine and cosine functions using field extension bases, providing a theoretical framework for understanding their algebraic properties.
Contribution
It introduces a novel algebraic approach to express sums of powers of sine and cosine in terms of field extension bases, advancing the theoretical understanding of these functions.
Findings
Expressions for sums of powers of sine and cosine in terms of field bases
Enhanced understanding of algebraic properties of trigonometric sums
Framework applicable to field extension analysis of trigonometric functions
Abstract
This paper presents expressions for sums of powers of sine and cosine in terms of the basis for the field extension obtained by adjoining the sine or cosine to the field of rational numbers.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics