Exsecant

Abstract: Trigonometry is a branch of mathematics that deals with relations between sides and angles of triangles. It has some relationship to geometry, though there is disagreement on exactly what that relationship is. For some, 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 rectangular trigonometry is introduced in order to be in the future a part of the General trigonometry topic. Thus, the definition of this original part is presented. The rectangular 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 rectangular 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 rectangular form with the internal and external circles formed by the intersection of the rectangular 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.

Abstract: The General Trigonometry is a new trend of trigonometry introduced by the author into the mathematical domain. It is introduced to replace the traditional trigonometry; it has huge advantages ahead the traditional one. It gives a general concept view of the trigonometry and forms an infinite number of trigonometry branches and each branch has its own characteristics and features. The concept of the General Trigonometry is completely different from the traditional one in which the study of angles will not be 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 geometrical form (e.g.: circle, elliptic, rectangle, quadrilateral ...) with the internal and external circles formed by the intersection of the geometrical 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. The most remarkable trigonometry branches are the "Elliptical trigonometry" and the "Rectangular trigonometry" introduced by the author and published by WSEAS. The importance of these trigonometry branches is that with one function, we can produce multi signal forms by varying some parameters. In this paper, an original study is introduced and developed by the author and some few examples are discussed only to give an idea about the importance of the General Trigonometry and its huge application in all scientific domains especially in Mathematics, Power electronics, Signal theory and processing and in Energy Economic Systems.

Abstract: (2007). A Geometric View of Complex Trigonometric Functions. The College Mathematics Journal: Vol. 38, No. 3, pp. 210-217.