<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

Online veröffentlicht: 07. Nov. 2022

Seitenbereich: 54 - 64

Eingereicht: 22. Juli 2022

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

Schlüsselwörter
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

Online veröffentlicht: 07. Nov. 2022

Seitenbereich: 54 - 64

Eingereicht: 22. Juli 2022

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

Schlüsselwörterelementary trigonometric functions

© 2022 Péter Medvegyev, published by Sciendo

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

Schlüsselwörter
elementary trigonometric functions