Integrating Rational Functions of Sine and Cosine Using the Rules of Bioche

Autor/in	Stewart, Seán M.
Titel	Integrating Rational Functions of Sine and Cosine Using the Rules of Bioche
Quelle	In: International Journal of Mathematical Education in Science and Technology, 53 (2022) 6, S.1688-1700 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Stewart, Seán M.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2021.1912841
Schlagwörter	Mathematics Instruction; Trigonometry; Mathematical Concepts; Equations (Mathematics); Problem Solving; Calculus + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Trigonometrie; Equations; Mathematics; Gleichungslehre; Problemlösen; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung
Abstract	For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions x [right arrow] -- x, [pi] -- x, and [pi] + x, allow one to decide which of the three trigonometric substitutions of: t = sin x, cos x, or tan x would be most appropriate for finding the integral. In seeking to not only bring these simple rules to the attention of a wider audience, formal justification of the rules is provided and two examples illustrating the use of the rules given. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01