设f(x)=asin(πx+α)+bcos(πx+β)+4(a,b,α,β均为非零实数),若f(2003)=6,求f(2008)的值
问题描述:
设f(x)=asin(πx+α)+bcos(πx+β)+4(a,b,α,β均为非零实数),若f(2003)=6,求f(2008)的值
答
f(2003)=asin(2003π+α)+bcos(2003π+β)+4
=asin(π+α)+bcos(π+β)+4
=-asin(α)-bcos(β)+4=6
所以asin(α)+bcos(β)=-2
f(2008)=asin(2008π+α)+bcos(2008π+β)+4
=asin(α)+bcos(β)+4=-2+4=2