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sci.Taylor-series-sine Calculator
Calculates the Taylor series approximation of sin(x) = x − x³/3! + x⁵/5! − ... and the truncation error at a given order. Taylor series for sin(x) converges for all x — 10-term series is accurate to < 10⁻¹⁵ for |x| < π; more terms are needed for larger |x| due to cancellation.
Inputs
X Rad
Reference formula or conversion factor shown for context.
N Terms
Count of items or occurrences.
Results
Taylor series sin(x) (
Sample size or count used in the calculation.
exact sin(x)
Sample size or count used in the calculation.
absolute error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
sin(x) = x - x³/3! + x⁵/5! - ...
Sample size or count used in the calculation.
radius of convergence
The computed radius -- half the diameter.
rule of thumb
A widely used practical approximation or heuristic for this field — useful for quick estimates but not a substitute for rigorous calculation.