设P={cos nπ/3,n∈Z},Q={sin(2k-3)π/6,k∈Z}.则集合P与Q的关系是:
问题描述:
设P={cos nπ/3,n∈Z},Q={sin(2k-3)π/6,k∈Z}.则集合P与Q的关系是:
烦请分析一下!
答
P周期是2π/(n/3)=6π/n
则n=1到6时
cos=1/2,-1/2,-1,-1/2,1/2,1
所以P={1/2,-1/2,-1,1}
同理
sin(2k-3)π/6
=cos[π/2-(2k-3)π/6]
=cos(π-kπ/3)
=-cos(kπ/3)
则Q也是{1/2,-1/2,-1,1}
所以P=Q