On Generalized Trigonometric Functions

Hisham Mahdi¹, Mohammed Elatrash¹ and Samar ELmadhoun^1,

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

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

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.

Keywords:
trigonometric functions generalized trigonometric functions trigonometric identities

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References:

[1]	Burgoyre F.D., “Generalization trigonometric functions.”, Mathematics of Computation, vol.18, pp 3-14-316,1964.
[2]	Edmunds D. and Lang J., “Generalizing trigonometric functions from different points of view,” http://www.math.osu.edu/mri/preprints/2009, Tech. Rep., 2009.
[3]	Lang J. and Edmunds D., “Eigenvalues, Embeddings and Generalised Trigonometric Functions”, Springer, 2011.
[4]	Shelupsky D., “A generalization of trigonometric functions.”, The American Mathematical Monthly, Vol.66 no. 10, pp 879-884,1959.
[5]	Wei D.,Elgindi Y. L..,and Elgindi M. B., “Some Generalized Trigonometric Sine Functions and Their Applications”, Applied Mathematical Sciences, Vol. 6, no. 122, 6053-6068, 2012.