Method for Solving the Differential Problem Related to Sine and Cosine Functions

Abstract

In this paper, we study the differential problems related to sine and cosine functions. The analytic forms of any order derivatives of two types of functions can be determined by using binomial series and differentiation term by term theorem. Moreover, two examples are proposed to demonstrate the calculations. The research method adopted in this study is to find the solutions through manual calculations and verify these answers using Maple.
Key Words: derivatives; sine and cosine functions, analytic forms; binomial series; differentiation term by term theorem; Maple