【題目】【2017山東高考理16】設(shè)函數(shù)，其中.已知.

（Ⅰ）求；

（Ⅱ）將函數(shù)的圖象上各點的橫坐標(biāo)伸長為原來的2倍（縱坐標(biāo)不變），再將得到的圖象向左平移個單位，得到函數(shù)的圖象，求在上的最小值.

【答案】（Ⅰ）.（Ⅱ）得最小值.

【解析】（Ⅰ）因為，

所以

由題設(shè)知，所以，.

故，，又，所以.

（Ⅱ）由（Ⅰ）知，，

將函數(shù)y=f（x）的圖象上各點的橫坐標(biāo)伸長為原來的2倍（縱坐標(biāo)不變），

得到函數(shù)的圖象；

再將得到的圖象向左平移個單位，得到的圖象，

∴函數(shù)；

當(dāng)x∈[﹣，]時，x﹣∈[﹣，]，∴sin（x﹣）∈[﹣，1]，

∴當(dāng)x=﹣時，g（x）取得最小值是﹣×=﹣．

【考點解讀】本題考查了兩角和與差的三角函數(shù)及三角函數(shù)圖象的變換與性質(zhì)。此類題目是三角函數(shù)問題中的典型題目。解答本題，關(guān)鍵在于能利用三角公式化簡函數(shù)、進(jìn)一步討論函數(shù)的性質(zhì)，本題易錯點在于一是圖象的變換與解析式的對應(yīng)，二是忽視設(shè)定角的范圍.難度不大，能較好的考查考生的基本運算求解能力及復(fù)雜式子的變形能力等。

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