Vol. 8, No. 3, 2015

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Two-parameter taxicab trigonometric functions

Kelly Delp and Michael Filipski

Vol. 8 (2015), No. 3, 467–480
Abstract

In this paper, we review some of the fundamental properties of the ${\ell }^{1}$, or taxicab, metric on ${ℝ}^{2}$. We define and give explicit formulas for two-parameter sine and cosine functions for this metric space. We also determine the maximum of these functions, which is greater than $1$.

Keywords
taxicab trigonometry, Minkowski geometry
Mathematical Subject Classification 2010
Primary: 51F99, 52A21