题目
题型:模拟题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075221-55623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075222-57121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075222-19072.png)
(1)求f(x)的最小值和单调区间;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075222-77339.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075223-24566.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075223-39062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075223-77978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075223-94901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075223-65734.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075224-83484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075224-38665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075224-88738.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075224-31533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075225-40247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075225-24699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075225-34958.png)
∵当2x﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075225-23493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075225-76456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075226-20640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075226-14414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075226-92227.png)
由﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075227-26605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075227-45183.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075227-87356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075227-72330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075227-93932.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075228-31697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075228-76885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075228-46441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075228-97481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075228-79270.png)
取k=0,结合
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075229-92065.png)
∴函数f(x)的单调增区间为[0,
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075229-54602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075229-88343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075229-69405.png)
(2)∵
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075230-69168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075230-27406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075230-47384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075230-64069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075231-83140.png)
∴sin(2x﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075231-30868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075231-92735.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075231-71879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075232-52402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075232-32983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075232-86578.png)
∵0<sin(2x﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075232-77360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075232-46477.png)
∴2x﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075233-63034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075233-88001.png)
∴cos(2x﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075233-50891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075233-55262.png)
∴sin2x=sin(2x﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075234-14606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075234-86075.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075234-42619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075234-76936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075234-80007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075235-64316.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075235-53822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075235-26449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075235-61797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075236-33093.png)
核心考点
试题【已知向量,函数,.(1)求f(x)的最小值和单调区间;(2)若,求sin2α的值.】;主要考察你对函数y=Asin(ωx+φ)的图象等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075201-63365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075202-34312.png)
(1)求函数f(x)的最小正周期;
(2)若y=f(x)的图象经过点
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075202-92893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075121-53739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075122-77050.png)
(1)求函数f(x)的周期及对称轴的方程;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075122-95398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075114-77635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075114-41835.png)
B.图象关于点(﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075115-74555.png)
C.图象关于点(﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075115-64838.png)
D.图象关于直线x=﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190920/20190920075115-53866.png)
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