已知函数f(x)=asin(πx+α﹚+bcos(πx+β﹚+4,且f(2004)=3,则f(2011)=__
问题描述:
已知函数f(x)=asin(πx+α﹚+bcos(πx+β﹚+4,且f(2004)=3,则f(2011)=__
答
此函数的周期是2,故f(0)=f(2004),f(1)=f(2011)
f(0)=asinα+bcosβ+4=3
f(1)=asin(π+α﹚+bcos(π+β﹚+4=-(asinα+bcosβ)+4=5
即f(2011)=5