f(x+π)=f(x)+sinx,0≤x

分类: 作业答案 • 2022-07-22 15:48:45

问题描述：

答

f(x+π)=f(x)+sinx
f(x+2π)=f(x+π)+sin(x+π)=f(x+π)-sinx=f(x)
所以推理的：f(x+nπ)=f(x)+nsinx
所以f(23π/6)=f[(-π/6)+4π]=f(-π/6)=f(-π/6)

答

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