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Lang J. and Edmunds D., “Eigenvalues, Embeddings and Generalised Trigonometric Functions”, Springer, 2011.

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Article

On Generalized Trigonometric Functions

1Department of Mathematics, Islamic University of Gaza, PO Box 108, Gaza, Palestine


Journal of Mathematical Sciences and Applications. 2014, Vol. 2 No. 3, 33-38
DOI: 10.12691/jmsa-2-3-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Hisham Mahdi, Mohammed Elatrash, Samar ELmadhoun. On Generalized Trigonometric Functions. Journal of Mathematical Sciences and Applications. 2014; 2(3):33-38. doi: 10.12691/jmsa-2-3-2.

Correspondence to: Samar  ELmadhoun, Department of Mathematics, Islamic University of Gaza, PO Box 108, Gaza, Palestine. Email: eng_samar1981@hotmail.com

Abstract

A new trigonometric functions called generalized trigonometric functions are perversely defined by a system of first order nonlinear ordinary differential equations with initial conditions. This system is related to the Hamilton system. In this paper, we define these functions using the equation , for m>0 We study the graphs, the trigonometric identities and some of common properties of these functions. We find the first derivatives which have different forms when is even and when is odd.

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