题目内容
已知向量



(Ⅰ)求ω的值.
(Ⅱ)设α是第一象限角,且


【答案】分析:(Ⅰ)利用向量的数量积,而二倍角公式以及两角和的正弦函数,化简数量积为
,利用周期求出ω的值.
(Ⅱ)设α是第一象限角,且
,化简方程为
,求出
,利用两角和的正弦函数,诱导公式化简
并求出它的值.
解答:解:(Ⅰ)由题意得
,
所以,
=
根据题意知,函数f(x)的最小正周期为3π,又ω>0,所以
(Ⅱ)由(Ⅰ)知
所以
解得
因为α是第一象限角,故
所以
点评:本题是基础题,考查向量的数量积的运算,三角函数的化简与求值,二倍角公式两角和的正弦函数公式的应用,为解题设置了障碍,细心解答.

(Ⅱ)设α是第一象限角,且




解答:解:(Ⅰ)由题意得

所以,


根据题意知,函数f(x)的最小正周期为3π,又ω>0,所以

(Ⅱ)由(Ⅰ)知


解得

因为α是第一象限角,故

所以

点评:本题是基础题,考查向量的数量积的运算,三角函数的化简与求值,二倍角公式两角和的正弦函数公式的应用,为解题设置了障碍,细心解答.

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