已知,cos0.70=a,cos0.71=b,则用线性插值法可求出cos0.702的近似值是多少?选项A,(a+4b)/5.B(4a+b0)/5C(a+3b)/4D(3a+b)/4

Question

已知,cos0.70=a,cos0.71=b,则用线性插值法可求出cos0.702的近似值是多少?
选项A,(a+4b)/5
.B(4a+b0)/5
C(a+3b)/4
D(3a+b)/4

Answer 1

根据公式ρ(x)=f(x0)+{[f(x1)-f(x0)] /(x1-x0)}*(x-x0)可得
cosx=cosx0+(cosx1-cosx0)(x-x0)/(x1-x0)
cos0.702= cos0.70+ (cos0.71- cos0.70)(0.702-0.70)/(0.71-0.70)
=a+0.002(b-a)/0.01
=0.8a+0.2b
=(4a+b)/5
选B