scholarly journals Relationship between Trigonometry Functions with Hyperbolic Function

2019 ◽  
Vol 1 (4) ◽  
pp. 82
Author(s):  
Sri Rejeki Dwi Putranti
Keyword(s):  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Complex Numbers ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Complex Functions ◽  
Engineering Problems ◽  
The Relationship

Many engineering problems can be solved by methods involving complex numbers and complex functions. In the definitions below we will prove the relationship between trigonometric functions and hyperbolic functions, where the hyperbolic function is an extension of the trigonometric function. Keywords: trigonometric functions; hyperbolic functions

scholarly journals The Extended MultipleG′/G-Expansion Method and Its Application to the Caudrey-Dodd-Gibbon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huizhang Yang ◽  
Wei Li ◽  
Biyu Yang
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Special Values ◽  
Wave Solutions ◽  
Complexiton Solutions ◽  
Hyperbolic Function Solutions

An extended multipleG′/G-expansion method is used to seek the exact solutions of Caudrey-Dodd-Gibbon equation. As a result, plentiful new complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions, and their mixture with arbitrary parameters are effectively obtained. When some parameters are properly chosen as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solutions.

scholarly journals Solutions of Fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov-Veselov Equations Using a Generalized Fractional Subequation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yanqin Liu ◽  
Limei Yan
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Rational Solutions ◽  
Coupled Equations ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Relationship Of ◽  
The Relationship

A new generalized fractional subequation method based on the relationship of fractional coupled equations is proposed. This method is applied to the space-time fractional coupled Konopelchenko-Dubrovsky equations and Nizhnik-Novikov-Veselov equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. It is observed that the proposed approach provides a simple and reliable tool for solving many other fractional coupled differential equations.

scholarly journals Researches about curves sketching on the perspective of global interpretation of figural units focusing on high school

2020 ◽  
Vol 22 (1) ◽  
pp. 61-87
Author(s):  
Bárbara Cristina Pasa ◽  
Méricles Thadeu Moretti
Keyword(s):  
High School ◽  
Quadratic Function ◽  
College Teaching ◽  
Vertical Axis ◽  
Modular Function ◽  
Algebraic Expression ◽  
Trigonometric Functions ◽  
Visual Variables ◽  
Complex Functions ◽  
The Relationship

A teaching approach based on the global interpretation of figurative properties prioritizes the curve sketching and understanding from the conversions among algebraic, graphical and linguistic registers, more precisely the identification of basic units (graphical, symbolic and linguistic) and the verification of how they related with each other. Raymond Duval presents this approach in an outline work of a related linear function using a resource for the global interpretation of the parameters of the algebraic expression: , emphasizing the relationship between these parameters and the graphical visual variables: inclination direction, tracing angles with the axes, and tracing position relatively to the vertical axis origin. Other authors have proposed works under this perspective with a focus on High School. Among them: Moretti (2003), for the quadratic function; Silva (2008), for the exponential, logarithmic and trigonometric functions; Menoncini & Moretti (2017), for the modular function; Martins (2017), for curves whose expressions are in parametric form; Moretti, Ferraz & Ferreira (2008), for more complex functions of college teaching; and Pasa (2017), for polynomial functions of the second and third degree. In this article, we present these works, complementing Pasa & Moretti (2016), presenting the resources used in each of them that allow changing verifications which the graph changes generates in the algebraic expression and vice versa and the identification of the visual variables and units related to the modifications.

scholarly journals Winding Numbers, Unwinding Numbers, and the Lambert W Function

2021 ◽  
Author(s):  
A. F. Beardon
Keyword(s):  
Complex Plane ◽  
Complex Number ◽  
Lambert W Function ◽  
Complex Numbers ◽  
Winding Number ◽  
Line Integral ◽  
Complex Functions

AbstractThe unwinding number of a complex number was introduced to process automatic computations involving complex numbers and multi-valued complex functions, and has been successfully applied to computations involving branches of the Lambert W function. In this partly expository note we discuss the unwinding number from a purely topological perspective, and link it to the classical winding number of a curve in the complex plane. We also use the unwinding number to give a representation of the branches $$W_k$$ W k of the Lambert W function as a line integral.

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

scholarly journals A Variety of Explicit Exact and Soliton Type Solutions of Conformable Fractional Equal-Width Equations

2018 ◽  
Author(s):  
Alper Korkmaz ◽  
Asim Zafar ◽  
Hadi Rezazadeh
Keyword(s):  
Fluid Dynamics ◽  
Surface Waves ◽  
Space Time ◽  
Function Approach ◽  
Hyperbolic Function ◽  
Trigonometric Functions ◽  
Conformable Derivative ◽  
Wave Type

Exact and soliton type solutions have great importance in propagation of surface waves, fluid dynamics, optics, and many other elds of nonlinear sciences. In this study, the explicit and exact soliton type solutions for two space-time fractional Equal- Width (FEW) equations with conformable derivative are procured via the hyperbolic function approach. The wave type solutions are represented in some hyperbolic and trigonometric functions.

scholarly journals p-Trigonometric andp-Hyperbolic Functions in Complex Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-18
Author(s):  
Petr Girg ◽  
Lukáš Kotrla
Keyword(s):  
Differential Equations ◽  
Complex Domain ◽  
Trigonometric Functions ◽  
Maclaurin Series ◽  
Hyperbolic Functions

We study extension ofp-trigonometric functionssinpandcospand ofp-hyperbolic functionssinhpandcoshpto complex domain. Our aim is to answer the question under what conditions onpthese functions satisfy well-known relations for usual trigonometric and hyperbolic functions, such as, for example,sin(z)=-i·sinh⁡i·z. In particular, we prove in the paper that forp=6,10,14,…thep-trigonometric andp-hyperbolic functions satisfy very analogous relations as their classical counterparts. Our methods are based on the theory of differential equations in the complex domain using the Maclaurin series forp-trigonometric andp-hyperbolic functions.

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