Calculations of Some Trigonometric Interpolation Polynomials and Some Graphical Representations in Maple

Technology and the use of software in the educational process are becoming increasingly more important in recent times. This article aims to demonstrate how to use the program Maple to solve some mathematical problems and in the process of teaching mathematics. This program isn't only a computing environment, but also a useful tool for teachers and students, for lectures, training, projects, etc. The author presents how Maple can be used to calculate some trigonometric polynomials and how to create some graphical representations in this program. Trigonometric polynomials and Fourier trigonometric series are tools of numerical methods and mathematical analysis and are used by engineers in the numerical processing of electric signals and images. Calculating the coefficients of trigonometric polynomials with traditional methods could take a long time, which is why programs such as Maple could help students, professors, engineers, etc. to calculate them faster. There are multiple programs (Derive, MathCad, Mathematica, SPSS, WinQSB, GeoGebra, C++, Python, Maxima, Scilab, Axiom, Geometer's Sketchpad, TKSolver, Bertini, MuPAD, CoCoA, Macaulay2, SageMath, Singular, Simulink, GraphThing, Graph Interface(GRIN), Delphi, Java, etc.) specialized in solving mathematical problems, however, in this article, the author has chosen Maple as an example of a program with a very wide academic distribution. The author created new abstract examples, aiming to contribute to the specialty literature by creating new examples of how to use Maple. The article recommends the use of Maple and other related programs for assisted instruction in the teaching and learning of mathematics, for particular cases of numerical methods and graphs respectively; and notes the need for the education system to integrate blended teaching and learning methods, in which computer programs are used together with traditional teaching methods, to improve the teaching process for mathematics.