Far East Journal of Mathematical Education

The Far East Journal of Mathematical Education is a peer-reviewed journal focused on mathematical education. It publishes research papers that enhance understanding of mathematical concepts and encourages the use of technology, statistics, algorithms, and simulations in mathematics learning.

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TANGENT FUNCTION AS A SOLUTION OF A 3-DIMENSIONAL FUNCTIONAL EQUATION

Authors

  • Hang Su
  • Ramesh Sharma

Keywords:

trigonometric identity, tangent function, functional equation, differential equation.

DOI:

https://doi.org/10.17654/0973563123016

Abstract

Taking a clue from the identity for the tangent of the sum of three angles, we form a corresponding functional equation in three variables. Assuming the function to be differentiable, we solve the functional equation and conclude that the solution is essentially the tangent function up to a constant multiple of the argument variable and a translation. This article involves trigonometry, multivariable calculus, differential equation and functional equation. The concept and methodology used can be understood by a student with a good background in multivariable calculus and differential equation. Teachers may also use this to stimulate further interest in students while teaching multivariate calculus and differential equation.

Received: October 5, 2023
Accepted: November 3, 2023

References

J. Aczél, On Applications and Theory of Functional Equations, Elsevier, 1969.

J. Aczél and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.

E. Castillo, J. M. Gutiérrez and A. Iglesias, Solving a functional equation, Mathematica J. 5 (1995), 82-86.

C. Efthimiou, Introduction to functional equations: theory and problem-solving strategies for mathematical competitions and beyond, American Mathematical Society and Mathematical Sciences Research Institute, 2011.

D. Singhal, The tangent function through a functional equation, Internat. J. Math. Ed. Sci. Tech. 32 (2001), 439-440.

C. G. Small, Functional Equations and how to Solve Them, Springer Science and Business Media, 2007, 131 pp.

B. J. Venkatachala, Functional Equations: A Problem Solving Approach, Prism Publications, 2008.

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Published

15-11-2023

Issue

Vol. 25 (2023)

Section

Articles

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Copyright (c) 2023 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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How to Cite

TANGENT FUNCTION AS A SOLUTION OF A 3-DIMENSIONAL FUNCTIONAL EQUATION. (2023). Far East Journal of Mathematical Education, 25, 57-61. https://doi.org/10.17654/0973563123016

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