f(x)=αsin(πx+α)+bcos(πx+β),其中α,β,a,b,都是非零常数,若f(2011)=-1,求f(2012)

问题描述:

f(x)=αsin(πx+α)+bcos(πx+β),其中α,β,a,b,都是非零常数,若f(2011)=-1,求f(2012)

f(2011)=asin(2011π+α)+bcos(2011π+β)
=asin(π+α)+bcos(π+β)= -(asinα+bcosβ)=-1
f(2012)=asin(2012π+α)+bcos(2012π+β)=asinα+bcosβ=1