设集合M={α|α=kπ2-π3,k∈Z},N={α|-π<α<π},则M∩N=______.-数学

题目简介

设集合M={α|α=kπ2-π3,k∈Z},N={α|-π<α<π},则M∩N=______.-数学

题目详情

设集合M={α|α=
2
-
π
3
,k∈Z},N={α|-π<α<π},则M∩N=______.
题型:填空题难度:中档来源:不详

答案

由-π<class="stub"kπ
2
-class="stub"π
3
<π得-class="stub"4
3
<k<class="stub"8
3
,∵k∈Z,
∴k=-1,0,1,2,即α=-class="stub"5
6
π,-class="stub"π
3
class="stub"π
6
class="stub"2
3
π.
则M∩N={-class="stub"5
6
π,-class="stub"π
3
class="stub"π
6
class="stub"2
3
π}.
故答案为:{-class="stub"5
6
π,-class="stub"π
3
class="stub"π
6
class="stub"2
3
π}

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