已知f(x)=asin(πx+α)+bcos(πx+β),若f(2007)=5,求f(2008)的值.

f(2007)=asin(2007π+α)+bcos(2007π+β) =asin(π+α)+bcos(π+β) =-asinα-bcosβ=5 f(2008)=asin(πx+α)+bcos(πx+β) =asin(2008π+α)+bcos(2008π+β) =asinα+bcosβ =-5