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Math. Comput. Appl. 2018, 23(3), 37; https://doi.org/10.3390/mca23030037

Applying Computer Algebra Systems in Approximating the Trigonometric Functions

1
Department of Mathematics, College of Natural Sciences, Cantho University, 3/2 Street, Cantho City, Vietnam
2
Department of Mathematics and Science, Holy Names University, 3500 Mountain Blvd., Oakland, CA 94619, USA
*
Author to whom correspondence should be addressed.
Received: 8 June 2018 / Revised: 9 July 2018 / Accepted: 12 July 2018 / Published: 14 July 2018
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Abstract

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 approximating π with 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. View Full-Text
Keywords: approximation; approximate value; Taylor polynomial; pointwise approximate polynomial; piecewise approximate polynomial approximation; approximate value; Taylor polynomial; pointwise approximate polynomial; piecewise approximate polynomial
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Quan, L.P.; Nhan, T.A. Applying Computer Algebra Systems in Approximating the Trigonometric Functions. Math. Comput. Appl. 2018, 23, 37.

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