Inextricably Linked: A Trigonometric Coupling

Authors

John Engbers, Marquette UniversityFollow
Adam Hammett, Cedarville University
Ian Hogan, Kent State University

Document Type

Article

Publication Date

2020

Publisher

Taylor & Francis

Source Publication

Mathematics Magazine

Source ISSN

0025-570X

Original Item ID

DOI: 10.1080/0025570X.2020.1826847

Abstract

Inspired by the classroom capsule and its follow-up, we present direct geometric derivations of the integral formulas for both the inverse hyperbolic and inverse polar trig functions, the latter being a new approach independent of Insel’s work. In so doing, we show that these two trigonometric settings are linked in a natural analytical geometric way, establishing a coordinate system determined by hyperbolas that is akin to polar coordinates. We then use the integral formulas to obtain the derivatives of the various hyperbolic and polar trig functions.

Comments

Mathematics Magazine, Vol. 93, No. 5 (2020): 352-362. DOI.

Recommended Citation

Engbers, John; Hammett, Adam; and Hogan, Ian, "Inextricably Linked: A Trigonometric Coupling" (2020). Mathematical and Statistical Science Faculty Research and Publications. 128.
https://epublications.marquette.edu/math_fac/128