Question

用四阶泰勒公式求sin29°

Answer 1

问：用四阶泰勒公式求sin29°

答：f(x)=f(x0)+f'(x0)/1!*(x-x0)+f''(x0)/2!*(x-x0)^2+…+f^(n)(x0)/n!(x-x0)^n+o((x-x0)^n) 取上右式前三项，如下： sin29=sin(28+1)=sin28+(sin28)'x(3π/180)+(sin28)''x(3π/180)^2/2 =0.5+πcos30/60-π^2xsin3067200 =0.5+π√3/120-π^2/14400 ≈0.483 附：精确6位有效数值 sin29度=0.483642