The Derivative of the Sine and Cosine. A New Derivation Approach

TL;DR

This paper introduces a novel method for deriving the derivatives of sine and cosine functions by utilizing Leibniz's early calculus principles, predating traditional derivations by Cotes and Euler.

Contribution

It presents a new derivation approach based on Leibniz's original discoveries, offering historical insight and alternative mathematical techniques.

Findings

Derivatives of sine and cosine derived using Leibniz's product, quotient, and chain rules.

The method predates and differs from classical derivations by Cotes and Euler.

Provides a historical perspective on calculus development.

Abstract

A new method is presented for finding the derivative of the sine and cosine using the discoveries of Leibniz in calculus between the years 1675 and 1677, namely the derivative of the product and the quotient of two functions as well as the chain rule, yet long before the discovery of the derivative of the sine by Roger Cotes in 1722 and Euler in 1748.