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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 kp, 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.


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (

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