Exact Expressions for Trigonometric Functions

SummarySolving polynomial equations and trigonometry are typically taught in separate modules or even separate classes. The derivation of a one-third angle formula gives students the opportunity to tie these two topics together. An algorithm for finding the cosine of one-third of a prescribed angle...

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Bibliographic Details
Published inThe College mathematics journal Vol. 55; no. 1; pp. 40 - 45
Main Authors Sathish Indika, S H, Leemis, Lawrence M
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis Ltd 01.01.2024
Subjects
Algorithms
Applied mathematics
Formulas (mathematics)
Mathematical analysis
Polynomials
Trigonometric functions
Trigonometry
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Summary:SummarySolving polynomial equations and trigonometry are typically taught in separate modules or even separate classes. The derivation of a one-third angle formula gives students the opportunity to tie these two topics together. An algorithm for finding the cosine of one-third of a prescribed angle is based on Cardano’s formula. In addition, we show how this algorithm can be combined with half, double, and triple angle formulas to give exact expressions for trigonometric functions written in terms of radicals for an infinite number of angles between 0 and π/2.
ISSN:0746-8342
1931-1346
DOI:10.1080/07468342.2023.2241316