Can we admit the way in which $\sin(x)$ is typically defined?

TL;DR

This paper examines the foundational definitions of sine and cosine, demonstrating that they can be derived from elementary geometric principles rather than relying solely on their traditional definitions.

Contribution

It shows that the standard facts about sine and cosine can be proved using basic elementary geometry, questioning the conventional assumptions.

Findings

Sine and cosine definitions can be derived from elementary geometry.

Traditional facts about sine and cosine are provable from basic geometric principles.

The paper challenges the necessity of standard definitions for sine and cosine.

Abstract

I review some facts which the usual sen(x) and cos(x) definitions are based on. The purpose of this paper is to show that this facts can be proved if we assume some basic ideas of elementary geometry.