已知函数f(x)=asin(πx+a)+bcos(πx+β)+1,且f(2012)=2012,求(2013)的值
问题描述:
已知函数f(x)=asin(πx+a)+bcos(πx+β)+1,且f(2012)=2012,求(2013)的值
答
解 f(2012)=asin(2012π+α)+bcos(2012π+β)+1
=asinα+bcosβ+1
所以asinα+bcosβ=2011
f(2013)=asin(2013π+α)+bcos(2013π+β)+1
=asin(π+α)+bcos(π+β)+1
=-(asinα+bcosβ )+1
=-2011+1
=-2010