WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Introduction to the Elliptical Trigonometry in Euclidian 2D-space with Simulation of Four Elliptical Trigonometric Functions Jes, Jes-x, Mar and Rit
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Abstract: Trigonometry is a branch of mathematics that deals with relations between sides and angles of triangles. The trigonometric functions are very important in technical subjects like Astronomy, Relativity, science, engineering, architecture, and even medicine. In this paper, the elliptical trigonometry is introduced in order to be in the future a part of the General Trigonometry topic. The concept of the Elliptical 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 an ellipse form with the internal and external circles formed by the intersection of the ellipse 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