Question

一道高一数学题，急啊！！！

设f(x)=｛sin(π/2 x+π/4)(x≤2007)
｛f(x－4)(x＞2007)
求f(2006)+f(2007)+f(2008)+f(2009)的值
f(x)是方程组

要详细的解答过程

Answer 1

f(2006)+f(2007)+f(2008)+f(2009)
=sin(2006π/2+π/4)+sin(2007x/2+π/4)+f(2004)+f(2005)
=sin(2006π/2+π/4)+sin(2007π/2+π/4)+sin(2004π/2+π/4)+sin(2005π/2+π/4)
=sin(1004π-π+π/4)+sin(1004π-π/2+π/4)+sin(1002π+π/4)+sin(1002+π/2+π/4)
=sin(-3π/4)+sin(-π/4)+sin(π/4)+sin(3π/4)
=0