函数y=sinπ/2x×sin[π/2(x-1)]的最小正周期是

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函数y=sinπ/2x×sin[π/2(x-1)]的最小正周期是
函数y=sinπ/2x×sin[π/2(x-1)]的最小正周期是

函数y=sinπ/2x×sin[π/2(x-1)]的最小正周期是
y=sin(π/2x)cos[π/2(x-1)]
=sin(π/2x)cos(π/2x-π/2)
=sin(π/2x)cos(π/2-π/2x)
=sin(π/2x)*sin(π/2x)
=[sin(π/2x)]^2=(1/2)(1-cosπx)
所以函数y=sin(π/2x)cos[π/2(x-1)]的最小正周期是：2.
函数y=cosπ/2x×cosπ/2(x-1)的最小正周期
如果是：函数y=cosπ/2x×cos[(π/2)(x-1)]的最小正周期
则有如下：
y=cosπ/2x×cosπ/2(x-1)
=cosπx/2*cos(πx/2-π/2)
=cosπx/2*cos(π/2-πx/2)
=cosπx/2*sinπx/2
=(1/2)sin(2*πx/2)
=(1/2)sinπx
ω=π,所以周期T=2π/ω=2
周期为2.

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