Question

设函数f(x)=asin(π x+a)+bcos(π x+ß),

其中a,b.ßa.都是非零实数,且满足f(2001)= - 2008,求f(2008)的值谢谢

Answer 1

函数f(x)=asin(π x+a)+bcos(π x+ß),
∵f(2001)= - 2008
∴asin(2001π+α)+bcos(2001π+β)
=asin(π+α)+bcos(π+β)
=-asinα-bcosβ
=-2008

∴asinα+bcosβ=2008
∴f(2008)=asin(2008π+α)+bcos(2008π+β)
=asinα+bcosβ=2008