高三-數(shù)學(xué)-大題專項(xiàng)訓(xùn)練三角函數(shù)-文檔

1、三角函數(shù)解答題1已知向量1(1cos)(sin)4axbx??????（1）當(dāng)[0]4x??時，若ab???，求x的值；（2）定義函數(shù)()()()fxaabxRfx???????求的最小正周期及最大值。2已知函數(shù)()cos(2)2sin()sin()344fxxxx????????（Ⅰ）求函數(shù)()fx的最小正周期和圖象的對稱軸方程；（Ⅱ）求函數(shù)()fx在區(qū)間[]122???上的值域。解：（1）()cos(2)2sin()sin()344

2、fxxxx?????????13cos2sin2(sincos)(sincos)22xxxxxx?????2213cos2sin2sincos22xxxx????13cos2sin2cos222xxx???sin(2)6x???22周期T????∴由2()()6223得kxkkZxkZ????????????∴函數(shù)圖象的對稱軸方程為()3xkkZ?????（2）5[]2[]122636xx????????????因?yàn)?)sin(2)6f

3、xx???在區(qū)間[]123???上單調(diào)遞增，在區(qū)間[]32??上單調(diào)遞減，所以當(dāng)3x??時，()fx取最大值1322???B3???B??sin2coscos2sinsin23fxxBxBx???????????222232kxk??????????∴函數(shù)的單調(diào)遞增區(qū)間是51212kk????????????（Ⅱ）得，由余弦定理acbcaBbB2cos23222???????0422????acca又acca222???代入上式得：4?

4、ac（當(dāng)且僅當(dāng)2??ca時等號成立）343sin21????acBacSABC（當(dāng)且僅當(dāng)2??ca時等號成立）5已知函數(shù)231()sin2cos22fxxx???()xR?（I）求函數(shù)()fx的最小值和最小正周期；（II）設(shè)ABC?的內(nèi)角ABC的對邊分別為abc，且3c?，()0fC?，若向量與向量共線，求ab的值.)sin1(Am?)sin2(Bn?解：（I）31cos21()sin2222xfxx????=sin(2)16x???則