Question

已知函数f（x）=asina(πx+α）+bcos(πx+β），其中a,b,α，β都是非零实数，且满足f(2010)=-1,

试求f(2011)的值

Answer 1

f（x）=asina(πx+α）+bcos(πx+β）
f(2010)=asin(2010π+α)+bcos(2010π+β)=-1
aisnα+bcosβ=-1
f(2011)=asin(2011π+α)+bcos(2011π+β)
=-(aisnα+bcosβ)
=-(-1)
=1