Question

1.f(x)=a sin(πx+α)+b con(πx+β),其中a,b,α,β都是不为0的实数,且满足f(2000)=

Answer 1

1.f(2000)=a sin(2000π+α)+b con(2000π+β)=asinα+bcosβ=-1

同理f(2002)=-1

(思路:别忘了y=sinx y=cosx的最小正周期是2π)

2.原式=sin(π/3)+sin(2π/3)+sin(3π/3)+...+sin(2004π/3)

∵T=6 ∴原式=334[sin(π/3)+sin(2π/3)+sin(3π/3)+sin(4π/3)+sin(5π/3)+sin(6π/3)]=334*(根号3/2+根号3/2+0-根号3/2-根号3/2+0)=0(思路:还是用到周期,最小正周期是6,从1-2004刚好是6的334倍,因此算前6个再乘以334就OK)