Version 1
: Received: 7 March 2023 / Approved: 8 March 2023 / Online: 8 March 2023 (06:25:57 CET)
How to cite:
Azim, M.; Akter Akhi, A.; Kamrujjaman, M. A Series of New Formulas To Approximate the Sine and Cosine Functions. Preprints2023, 2023030146. https://doi.org/10.20944/preprints202303.0146.v1
Azim, M.; Akter Akhi, A.; Kamrujjaman, M. A Series of New Formulas To Approximate the Sine and Cosine Functions. Preprints 2023, 2023030146. https://doi.org/10.20944/preprints202303.0146.v1
Azim, M.; Akter Akhi, A.; Kamrujjaman, M. A Series of New Formulas To Approximate the Sine and Cosine Functions. Preprints2023, 2023030146. https://doi.org/10.20944/preprints202303.0146.v1
APA Style
Azim, M., Akter Akhi, A., & Kamrujjaman, M. (2023). A Series of New Formulas To Approximate the Sine and Cosine Functions. Preprints. https://doi.org/10.20944/preprints202303.0146.v1
Chicago/Turabian Style
Azim, M., Asma Akter Akhi and Md Kamrujjaman. 2023 "A Series of New Formulas To Approximate the Sine and Cosine Functions" Preprints. https://doi.org/10.20944/preprints202303.0146.v1
Abstract
We approximate the trigonometric function sine and cosine on the interval . This analysis provides two formulas to approximate sine and cosine. At first, we try to derive the formula which involves a square root, and then we derive another formula that does not require any use of a square root. Nevertheless, after deriving the procedure which requires no square root, we further try to increase its accuracy and then derive another formula that approximates trigonometric functions more accurately on the interval [0, pi/2]. So, this analysis provides mainly two types of procedures. One uses square roots, whereas the other does not. We also focus on ensuring the accuracy of these trigonometric functions in the interval [0,pi/2]. This accuracy analysis is portrayed using the graph. This graph shows the difference between the values generated by the functions defined here and the actual value of these functions. So, these graphs also indicate the error of these functions on that interval. Finally, we compare our approximation with the approximation formula of the 7th-century Indian Mathematician Bhaskara I.
Keywords
sine; cosine; Bhaskara I’s formula
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
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.
