Trigonometric Angle-Sum Formulas and Conformal Maps

Greg Markowsky; David Treeby

doi:10.1080/07468342.2023.2201563

Trigonometric Angle-Sum Formulas and Conformal Maps

Greg Markowsky
, David Treeby

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Summary: The trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.

Original language	English
Pages (from-to)	195-199
Number of pages	5
Journal	College Mathematics Journal
Volume	54
Issue number	3
DOIs	https://doi.org/10.1080/07468342.2023.2201563
Publication status	Published - 3 May 2023

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10.1080/07468342.2023.2201563

Cite this

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title = "Trigonometric Angle-Sum Formulas and Conformal Maps",

abstract = "Summary: The trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.",

author = "Greg Markowsky and David Treeby",

note = "Funding Information: The first author is grateful to Paul Cally for useful conversations, and also for support from Australian Research Council Grants DP0988483 and DE140101201. We are also grateful to several anonymous referees, whose suggestions have significantly improved the article. Publisher Copyright: {\textcopyright} 2023 The Mathematical Association of America.",

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N2 - Summary: The trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.

AB - Summary: The trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.

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Trigonometric Angle-Sum Formulas and Conformal Maps

Abstract

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Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

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Trigonometric Angle-Sum Formulas and Conformal Maps

Abstract

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Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this