f(x+π)=f(x)+sinx,0≤x

题目

f(x+π)=f(x)+sinx,0≤x

答案

原式=f(17π/6+π)
=f(17π/6)+sin17π/6
=f(11π/6+π)+sin17π/6
=f(11π/6)+sin11π/6+sin17π/6
同理
=f(5π/6)+sin5π/6+sin11π/6+sin17π/6
=0+1/2-1/2+1/2
=1/2