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.
Quan, L. P., & Nhan, T. A. (2018). Applying Computer Algebra Systems in Approximating the Trigonometric Functions. Math. Comput. Appl., 23(3), 37. https://doi.org/10.3390/mca23030037