Approximating cosine and sine functions numerically

By Hans Rudolf Schneebeli

Switzerland

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Abstract

Abstract:

How can function values ​​for sine or cosine be quickly and reliably numerically estimated?  We consider equal circular motions on the unit circle in the complex plane and find sine and cosine as solutions of a differential equation. The two functions can be numerically approximated in a hybrid procedure at the same time. Euler’s method will be used to this case. The goal is a numerical method which is stable and leads quickly to functional values ​​with at least 12 valid decimal places.

The paper is in German with the title, "Cosinus und Sinus numerisch effizient annahern."  

Hans R. Schneebeli was born in 1946 in Zurich, Switzerland and obtained the following degrees: MSc Mathematics ETH Zuerich 1972 and PhD Mathematics ETH Zurich 1977  in homological methods in group theory.

He taught mathematics from 1978-2011 at the pre-university level in Switzerland with a special interest in relevant applications accessible in High School/College, motivated by publications such as UMAP-modules. He is retired and is now a potter.

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Researchers should cite this work as follows:

  • Hans Rudolf Schneebeli (2018), "Approximating cosine and sine functions numerically," https://simiode.org/resources/4437.

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