How Does a Computer Calculate sin(x)?

Yaroslav Vakula

This dashboard analyzes the approximation of \(\sin(x)\) using Maclaurin series.

Key Features:

Interactive visualization of polynomial convergence.
Analysis across the interval \([-2\pi, 2\pi]\).

The Maclaurin series is defined as: \[\sin(x) \approx \sum_{n=0}^{N} \frac{(-1)^n x^{2n+1}}{(2n+1)!}\]

Technical Insight:

For \(n=13\), the approximation is virtually indistinguishable from the actual function in the range \([-\pi, \pi]\). However, note how quickly the error grows outside this “safe” zone.

Target Function sin(x)

Convergence of Taylor Polynomials