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On Fundamental Errors in Trigonometry

Author:

Kalanov, Temur Z.

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

June 20, 2022

File:

/Research Papers-Mathematics and Applied Mathematics/Download/9243

Downloads:

287

Keywords:

general mathematics, trigonometry, geometry, methodology of mathematics, mathematical physics, physics, engineering, formal logic, dialectics, philosophy of mathematics, philosophy of science

Abstract:

The critical a nalysis of the foundations of standard trigonometry is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) trigonometry does not treat a right triangle as a material system. Therefore, trigonometry does not satisfy the system principle; ( 2) trigonometric functions do not satisfy the mathematical definition of a function. The terms “sine”, “cosine”, “tangent”, “cotangent” and others are not identical to the concept of function. Symbols “cos”, “sin”, “tg”, “ctg”, etc. indicate only that there is a correspondence (connection) between the values of the quantities of the angle and the lengths of the sides in a right -angled triangle . Therefore, the standard definitions of trigonometric functions do not represent mathematical (quantitative) relationships between the quantities of the angle and the lengths of the sides in a right-angled triangle. Trigonometric functions are neither explicit nor implicit functions; (3) the range of definition of trigonometric functions does not satisfy the condition for the existence of a right-angled triangle because the definitions of trigonometric functions contradict to the system principle..../...

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