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http://hdl.handle.net/20.500.12358/21370
TitleGeneralized Trigonometric Functions
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Abstract

A new trigonometric functions called generalized trigonometric functions are defined by system of first order nonlinear ordinary differential equations with initial conditions. This system is related to the Hamilton system. In this thesis, we identify new trigonometric functions using the equation │x│m + │y│m = 1, for m > 0. The main purpose of this thesis is generalizing the rules of the usual trigonometric functions to the new functions. We prove some properties and identities of these functions and graph these functions when 0<m<1, m = 1, and m > 1. When m=2, we notice that new functions coincide with the usual trigonometric functions. Moreover, we give relation formulas of these functions which depend on the usual trigonometric functions. We find the first derivative of these functions and prove that for m = 1, the generalized trigonometric functions y = sin1 θ and y = cos1 θ have no derivatives at θ = n; n ∈ Z. We find generalizing form of the first derivative of these functions when m is odd and when m is even. We notice that the derivatives are different. Throughout this study, we understand more about the theoretical framework of trigonometric functions.

Authors
EL-madhoun, Samar Ibrahim
Supervisors
Mahdi, Hisham
ELatrash, Mohammed S.
Typeرسالة ماجستير
Date2014
LanguageEnglish
Publisherالجامعة الإسلامية - غزة
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  • PhD and MSc Theses- Faculty of Science [445]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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