General Mathematics

    

Different Approaches for Proving the Pythagorean Theorem Using Trigonometry

Authors: Tathagata Biswas

Contrary to the claims by Elisha S Loomis in his famous book and popular belief, several approaches towards proving the Pythagorean theorem using trigonometry exists. These approaches essentially use trigonometric identities and concepts that can be derived independent of the identity {sin}^2x + {cos}^2x = 1, to avoid any circular reasoning. Crucial to the trigonometric approaches are the law of sines, trigonometric angle sum and difference identities and modern definitions of trigonometric functions using the power series and Euler’s formula. This article describes these trigonometric proofs of the theorem.

Comments: 8 Pages.

Download: PDF

Submission history

[v1] 2024-10-21 21:02:10

Unique-IP document downloads: 216 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus