Volume
22
Issue
3
Abstract
In this paper, we use elementary methods to derive a rational function over the integers to approximate the trigonometric sine function on the interval [0, π/2]. This formula can then be used to derive a quartic polynomial with a root close to π/3 , providing an interesting algebraic approximation to this value. A more accurate rational function over the reals is then computed using numerical optimization. This new formula, while more accurate, provides a worse approximation of π/3 in the corresponding quartic equation, showing the trade-offs in local vs. global approximation. This paper is accessible to undergraduates and illustrates a combination of mathematical constructions used in Algebra, Calculus and Numerical Optimization.
First Page
335
Last Page
342
Recommended Citation
Azim, Mashrur and Griffin, Christopher
(2025)
"Rational Approximations of Sine and Cosine,"
The Mathematics Enthusiast: Vol. 22
:
No.
3
, Article 17.
DOI: https://doi.org/10.54870/1551-3440.1673
Available at:
https://scholarworks.umt.edu/tme/vol22/iss3/17
Digital Object Identifier (DOI)
10.54870/1551-3440.1673
Publisher
University of Montana, Maureen and Mike Mansfield Library
