Applying Computer Algebra Systems in Approximating the Trigonometric Functions

Mathematical and Computational Applications

Nhan, Thái Anh¹  Quan, Le Phuong² 

[1] Department of Mathematics and Science, Holy Names University, 3500 Mountain Blvd., Oakland, CA 94619, USA;Department of Mathematics, College of Natural Sciences, Cantho University, 3/2 Street, Cantho City, Vietnam

关键词: approximation;    approximate value;    Taylor polynomial;    pointwise approximate polynomial;    piecewise approximate polynomial;   

DOI  :  10.3390/mca23030037

学科分类：计算数学

来源: mdpi

【 摘 要 】

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansion about a point having a form of k p, k ∈ Z and p = π / 2, and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximatingπwith a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE.

【 授权许可】

CC BY