Question

已知函数f(x)=asin(πx+α)+bcos(πx+β),其中a,b,α,β都是非零实数.f(2005)=-1,则f

Answer 1

f(x)=asin(πx+α)+bcos(πx+β)

f(2005)=asin(2005π+α)+bcos(2005π+β)=asin(π+α)+bcos(π+β)=-1

asin(π+α)+bcos(π+β)=-1

asin(α)-bcos(β)=-1

bcos(β)=asin(α)+1

f(2006)=asin(2006π+α)+bcos(2006π+β)=asin(α)+bcos(β)=asin(α)+asin(α)+1

=2asin(α)+1