Vol. 3 No. 2 (2023)

On Rational and Irrational Values of Trigonometric Functions

Published 2023-09-30


  • Trigonometry,
  • Trigonometric Functions,
  • Rational Number,
  • Irrational Number

How to Cite

Akarsu, V. (2023). On Rational and Irrational Values of Trigonometric Functions. Advanced Geomatics, 3(2), 56–62. Retrieved from https://publish.mersin.edu.tr/index.php/geomatics/article/view/988


The beginning of trigonometry goes back 4000 years from today. Today, there are Euclidean and Non-Euclidean trigonometry. It can be said that trigonometry emerged from the need to make maps containing the position information of the stars, to determine the time and to make a calendar, mostly in astronomy. Each of the six trigonometric functions is defined according to the directed plane angle. For each angle in the domain of these functions, their values correspond to a real number consisting of rational or irrational numbers. Trigonometric functions have an important position in basic sciences and technology as well as calculations in engineering and architecture. In addition to being a branch of mathematics, trigonometry is widely used in solving geometry and analysis problems. It has an indispensable importance in engineering and architectural design and calculations. The values of trigonometric functions are usually an irrational number, with the exception of some special angle values. Irrational numbers are numbers that are not proportional. In other words, they are numbers whose results are uncertain. Examples are numbers such as pi, e, and radical. The irrational values of trigonometric functions, which are infinite decimal expansions, are given in the tables by rounding them to only four or six digits. When entering the trigonometric function values in the tables (or the values obtained in the libraries of electronic calculators) into algebraic operations, the resulting numbers are approximated. In the article, besides showing that most of the trigonometric function values such as sinθ, cosθ and tanθ of many θ angles are irrational, the effect of these functions on the result values of calculations made in engineering and architecture is interpreted.


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