<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The article discusses the construction of the elementary trigonometric functions. It discusses several approaches, but the main message is that to construct the trigonometric functions one needs to follow the same approach as one should use during the construction of the real exponential function, but one should use complex numbers. The key point is that one must construct the complex square root function to define the trigonometric functions on the binary numbers and then one should use some convexity argument to prove their differentiability. This approach, as the power series approach, based on the intimate relation between the trigonometric and the exponential functions.</p>
</abstract>

The article discusses the construction of the elementary trigonometric functions. It discusses several approaches, but the main message is that to construct the trigonometric functions one needs to follow the same approach as one should use during the construction of the real exponential function, but one should use complex numbers. The key point is that one must construct the complex square root function to define the trigonometric functions on the binary numbers and then one should use some convexity argument to prove their differentiability. This approach, as the power series approach, based on the intimate relation between the trigonometric and the exponential functions.

On the construction of the elementary trigonometric functions

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the construction of the elementary trigonometric functions"}

The article discusses the construction of the elementary trigonometric functions. It discusses several approaches, but the main message is that to construct...

On the construction of the elementary trigonometric functions

Published Online: Nov 07, 2022

Page range: 54 - 64

Received: Jul 22, 2022

DOI: https://doi.org/10.2478/puma-2022-0024

Keywords
elementary trigonometric functions

© 2022 Péter Medvegyev, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the construction of the elementary trigonometric functions

Published Online: Nov 07, 2022

Page range: 54 - 64

Received: Jul 22, 2022

DOI: https://doi.org/10.2478/puma-2022-0024

Keywordselementary trigonometric functions

© 2022 Péter Medvegyev, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
elementary trigonometric functions