Deducing Trigonometric Functions from Differential Equations: An Educational Perspective

Authors

  • Sameen Ahmed Khan Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah, Sultanate of Oman
  • Manisha Kankarej Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah, Sultanate of Oman
  • Mohammad Nazrul Islam Khan Department of Computer Engineering, College of Computer Engineering, Qassim University, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6146

Keywords:

Trigonometric functions, Differential equations, Qualitative theory of differential equations, Oscillation phenomenon, Sturm separation theorem, Sturm comparison theorem, Orthogonal polynomials

Abstract

We derive sine and cosine trigonometric functions by exploring the qualitative properties of differential equations. Further we demonstrated that the two functions are periodic. Additionally we derived the sine and cosine of sums and differences of two angles from differential equations.  The oscillations of the solutions of second-order differential equations are examined along with related theorems and techniques.  

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Mathematics Education

License

Copyright (c) 2025 Sameen Ahmed Khan, Manisha Kankarej, Mohammad Nazrul Islam Khan

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How to Cite

Deducing Trigonometric Functions from Differential Equations: An Educational Perspective. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6146. https://doi.org/10.29020/nybg.ejpam.v18i4.6146