Question

设函数f(x)=asin(πx+α)+bcos(πx+β)(其中a,b,α,β为非零实数),若f(2006)=5,

Answer 1

f(x)=asin(πx+α)+bcos(πx+β) ,f(2006)=5,

即asin(2006π+α)+bcos(2006π+β) =5,

利用诱导公式得：asin(α)+bcos(β) =5.

∴f（2007）=asin(2007π+α)+bcos(2007π+β)

= asin(π+α)+bcos(π+β)

= -asin(α)-bcos(β)=-5.