Period of sin(x-[x])
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The period of sin(x) is 2π.
For f(x)=sin⌊x⌋, note that f(0)=0 only for x∈[0,1). For other values, f(x)=sin(n),n∈N. But sin(x)=0⟺x=kπ,k∈Z. Thus f(x) is never zero again, or the function is not periodic.
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