Bibliographic Details
| Title: |
Rational Approximations of Sine and Cosine. |
| Authors: |
Azim, Mashrur1 mashrurazimaornab83@gmail.com, Griffin, Christopher2 griffinch@psu.edu |
| Source: |
Mathematics Enthusiast. Oct2025, Vol. 22 Issue 3, p335-342. 7p. |
| Subject Terms: |
*Calculus, *Algebra, Trigonometric functions, Sine function, Quartic equations |
| 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/2, 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/2 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Education Research Complete |
