Elliptical Trigonometry

The Elliptical Trigonometry is an original study introduced by Claude Ziad Bayeh in 2004 and it is published by WSEAS Journal transaction on Mathematics. It is the general case of the traditional trigonometry. 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 opened 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. The main advantage of this new trigonometry is that it can describe a huge number of multi form periodic signals by varying 2 parameters which are not possible with the traditional trigonometry. It has huge applications such as Electronics, Electrical Engineering, Power Electronics, Signal Processing and all topics related to the trigonometry.

The Elliptical Trigonometry contains 32 principle functions, the main important functions are Ejes (Elliptic Jes) which is the general case of cosine (traditional trigonometry) and Emar (Elliptic Mar) which is the general case of sine (traditional trigonometry).

Important signals obtained using the function "Ejes":

Impulse train with positive and negative part, elliptic deflated, quasi-triangular, sinusoidal, elliptical swollen, square signal, rectangular signal, impulse train (positive part only), rectified elliptic deflated, saw signal, rectified elliptical swollen, continuous signal…