WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Introduction to the Rhombus Trigonometry in Euclidian 2D-space with simulation of four Rhombus trigonometric functions RhJes, RhJes-x, RhMar and RhRit
Author:
Abstract: The Rhombus Trigonometry is an original study introduced in the mathematical domain by the author. Trigonometry is a branch of mathematics that deals with relations between sides and angles of triangles. It has some relationships to geometry, though there is disagreement on exactly what is that relationship. For some scientists, trigonometry is just a subtopic of geometry. The trigonometric functions are very important in technical subjects like Astronomy, Relativity, Science, Engineering, Architecture, and even Medicine. In this paper, the Rhombus trigonometry is introduced in order to be a part of the General Trigonometry topic. Thus, the definition of this original part is presented, and the Rhombus trigonometric functions are also defined. The importance of these functions is by producing multi signal forms by varying some parameters of a single function. Different signals and forms are analyzed and discussed. The concept of the Rhombus Trigonometry is completely different from the traditional trigonometry in which the study of angles is not the relation between sides of a right triangle that describes a circle as the previous one, but the idea here is to use the relation between angles and sides of a rhombus form with the internal and external circles formed by the intersection of the rhombus form and the positive parts of x’ox and y’oy axis in the Euclidian 2D space and their projections. This new concept of relations will open a huge gate in the mathematical domain and it can resolve many complicated problems that are difficult or almost impossible to solve with the traditional trigonometry, and it can describe a huge number of multi-form periodic signals.
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Keywords: Mathematics, geometry, trigonometry, angular function, multi form signal, power electronics.