Evaluating trigonometric systems in triangles without using area factors

Abstract

This article evaluated the upper and lower bounder for trigonometric system in a triangle knowing the measures of their sides without area factors. First of all, a formula was set to compute the area of a triangle in terms of the sides of a given triangle; and provide formulas to calculate the radius of the inscribed circle - circumscribed circle of a triangle and evaluates the upper bounder of the altitude in the triangle. Next, the upper bounder was evaluated from the sin and tan trigonometric functions of the angles in the triangle. Finally, an evaluation was made of the lower bound of the trigonometric functions such as cosin and cotan of the angles in the triangle. Several examples will be applied to problems involving the trigonometric system evaluation are proposed to illustrate some of the main results.