Evaluating the Derivatives of Trigonometric Functions with Maple

This paper uses the mathematical software Maple for the auxiliary tool to study the differential problem of two types oftrigonometric functions. We can obtain the closed forms of any order derivatives of these two types of trigonometric functions byusing finite arithmetic-geometric series, Euler's formula and DeMoivre's formula, and hence greatly reduce the difficulty ofcalculating their higher order derivative values. In addition, we propose some examples to do calculation practically. The researchmethods adopted in this study involved finding solutions through manual calculations and verifying these solutions by usingMaple. This type of research method not only allows the discovery of calculation errors, but also helps modify the originaldirections of thinking from manual and Maple calculations. Therefore, Maple provides insights and guidance regarding problem solvingmethods.