The computer that landed Apollo 11 on the Moon computed sine with a polynomial of just three terms. sin(πx/2) ≈ 2((C₅x² + C₃)x² + C₁)x, used only for |x| ≤ 1. The constants are not Taylor coefficients. Taylor's C₃ would be −0.3229820, the AGC stored −0.3216147, nudged so the error wiggles across the interval instead of piling up at the end. Result: max error 1.1×10⁻⁴ versus 4.5×10⁻³ for Taylor, about 40 times better at the same cost. Good engineering often means choosing better constants.