Question

设f(x)=a*sin(πx+α)+b*COS(πx+β)+4(a ,b ,α ,β均为非零实数),若f(2003)=6

Answer 1

f(x+5)=a*sin(πx+5π+α)+b*COS(πx+5π+β)+4=-[a*sin(πx+α)+b*COS(πx+β)]+4

又f(x)=a*sin(πx+α)+b*COS(πx+β)+4

所以f(x+5)+f(x)=8

f(2008)+f(2003)=8

f(2008)=2