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

Access to Document

10.1080/07468342.2023.2201563

Cite this

@article{af2ea88591a344c7a92fc8636d0e5cde,

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.",

year = "2023",

month = may,

day = "3",

doi = "10.1080/07468342.2023.2201563",

language = "English",

volume = "54",

pages = "195--199",

journal = "College Mathematics Journal",

issn = "0746-8342",

publisher = "Taylor & Francis",

number = "3",

}

TY - JOUR

T1 - Trigonometric Angle-Sum Formulas and Conformal Maps

AU - Markowsky, Greg

AU - Treeby, David

N1 - 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: © 2023 The Mathematical Association of America.

PY - 2023/5/3

Y1 - 2023/5/3

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.

UR - http://www.scopus.com/inward/record.url?scp=85158823380&partnerID=8YFLogxK

U2 - 10.1080/07468342.2023.2201563

DO - 10.1080/07468342.2023.2201563

M3 - Article

AN - SCOPUS:85158823380

SN - 0746-8342

VL - 54

SP - 195

EP - 199

JO - College Mathematics Journal

JF - College Mathematics Journal

IS - 3

ER -

Trigonometric Angle-Sum Formulas and Conformal Maps

Abstract

Access to Document

Other files and links

Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this

Trigonometric Angle-Sum Formulas and Conformal Maps

Abstract

Access to Document

Other files and links

Projects

Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this