Martini, Horst, Wenzel, Walter : The Computation of Derivatives of Trigonometric functions via the Fundamental Theorem of Calculus

Author(s):

Martini, Horst, Wenzel, Walter

Title:

The Computation of Derivatives of Trigonometric functions via the Fundamental Theorem of Calculus

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2001

Mathematics Subject Classification:

26A09			[ Elementary functions ]
26A24			[ Differentiation : general theory, generalized derivatives, mean-value theorems ]
26A42			[ Integrals of Riemann, Stieltjes and Lebesgue type ]
70-01			[ Instructional exposition ]

Abstract:

We compute the derivatives of trigonometric functions by making use of several aids from analysis, but without using any nontrivial relationship between these functions. As an application, we prove an identity concerning sine and cosine by analysing some linear differential equation.

Keywords:

Trigonometric functions, differentiation and integration, rules for differentiation, the fundamental theorem of calculus, linear differential equations

Language:

English

Publication time:

1 / 2002