sin(x) approximated by successive Taylor polynomials
Each extra term extends the approximation further. Adding more terms: sin(x) ≈ x − x³/6 + x⁵/120 − x⁷/5040 + …
Key Maclaurin series and their radii of convergence
Table of Maclaurin series
| f(x) | Reihe | Radius |
|---|---|---|
| eˣ | 1+x+x²/2!+x³/3!+⋯ | ∞ |
| sin x | x-x³/3!+x⁵/5!-⋯ | ∞ |
| cos x | 1-x²/2!+x⁴/4!-⋯ | ∞ |
| ln(1+x) | x-x²/2+x³/3-⋯ | |x|≤1 |
| 1/(1-x) | 1+x+x²+x³+⋯ | |x|<1 |
cos(x) approximated by successive Taylor polynomials
cos(x) ≈ 1 − x²/2 + x⁴/24 − x⁶/720 + … Each pair of terms is one more order of accuracy.
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