Generalized trigonometric functions

Other Title(s)

الدوال المثلثية المعممة

Dissertant

al-Madhun, Samar Ibrahim

Thesis advisor

al-Atrash, Muhammad S.
Mahdi, Hisham B.

Comitee Members

al-Habil, Isa Diyab
Salim, Tariq Umar

University

Islamic University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (Gaza Strip)

Degree

Master

Degree Date

2014

English Abstract

-A new trigonometric functions called generalized trigonometric functions are de ned by system of rst order nonlinear ordinary di erential equations with initial conditions.

This system is related to the Hamilton system.

In this thesis, we identify new trigono- metric functions using the equation jxjm +jyjm = 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 nd the rst derivative of these functions and prove that for m = 1, the generalized trigonometric functions y = sin1 and y = cos1 have no derivatives at = n 2 ; n 2 Z.

We nd generalizing form of the rst derivative of these functions when m is odd and when m is even.

We notice that the derivatives are di erent.

Throughout this study, we understand more about the theoretical framework of trigono- metric functions

Main Subjects

Mathematics

Topics

• Algebra

No. of Pages

90

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-531378