题目
题型:不详难度:来源:
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-16933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-71750.png)
(2)若CB∥OP,求sin
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-83581.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-43592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-44132.png)
解析
因为四边形OAQP是平行四边形,
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-71750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-16933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-85849.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-16933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-71750.png)
又平行四边形OAQP的面积为S=|
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-16933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-85849.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-16933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-71750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-43592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-17442.png)
又0<θ<π,所以当θ=
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-43441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-16933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-71750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-43592.png)
(2)由题意,知
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-90445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-85849.png)
因为CB∥OP,所以cos θ=2sin θ.
又0<θ<π,cos2θ+sin2θ=1,解得sin θ=
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-26681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-73275.png)
所以sin2 θ=2sin θcos θ=
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-80916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-10229.png)
所以sin
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015126-83581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-30633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-30633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-80916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015129-96179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015128-10229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015129-16505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015127-44132.png)
核心考点
试题【A,B分别是单位圆与x轴、y轴正半轴的交点,点P在单位圆上,∠AOP=θ(0<θ<π),C点坐标为(-2,0),平行四边形OAQP的面积为S.(1)】;主要考察你对平面向量应用举例等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015120-60272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015120-41427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015120-62415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015121-43250.png)
A.2 | B.4 | C.6 | D.8 |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015113-13616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015113-11800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015114-27923.png)
(1)求a·b及|a+b|;
(2)若f(x)=a·b-2λ|a+b|的最小值为-
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015114-70298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015106-30486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015107-71715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015107-98277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015107-80848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015107-62102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015101-90046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015101-36316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015101-63524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015102-33765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015102-30750.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015101-90046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015102-85654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015102-48499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015103-31839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015055-68693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015055-13891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105015055-96760.png)
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