f(x+π)=f(x)+sinx,0≤x

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f(x+π)=f(x)+sinx,0≤x
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f(x+π)=f(x)+sinx,0≤x
f(x+π)=f(x)+sinx,0≤x

f(x+π)=f(x)+sinx,0≤x
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

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)