设函数f(x)=asin(πx+α)+bcos(πx=β),其中a、b、α、β都是不为零的实数,且满足f(2000)=-1,求f(2002)的值.

问题描述:

设函数f(x)=asin(πx+α)+bcos(πx=β),其中a、b、α、β都是不为零的实数,且满足f(2000)=-1,求f(2002)的值.

f(x)=asin(πx+α)+bcos(πx+β)
f(2000)=asin(2000π+α)+bcos(2000π+β)
=asinα+bcosβ
=-1
f(2001)=asin(2001π+α)+bcos(2001π+β)
=asin(π+α)+bcos(π+β)
=-asinα-bcosβ
=-(asinα+bcosβ)
=1