题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034028-30191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034028-44252.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034028-24238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-34923.png)
解析
试题分析:(1)由已知及向量数量积的坐标运算可求得
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-11148.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-29998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-87018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034030-94071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034030-58987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034030-61696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034028-44252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-87018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034030-11958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034030-58987.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034030-61696.png)
试题解析:(1) 因为a·b=2+sinθcosθ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034031-32972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034031-43572.png)
所以 (sinθ+cosθ)2=1+2 sinθcosθ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034031-52607.png)
又因为θ为锐角,所以sinθ+cosθ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034028-24238.png)
(2) 解法一 因为a∥b,所以tanθ=2.
所以 sin2θ=2 sinθcosθ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034031-58860.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034032-64811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034032-27149.png)
cos2θ=cos2θ-sin2θ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034032-59346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-94568.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-71776.png)
所以sin(2θ+
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-80463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-60534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034034-14666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-60534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034032-27149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034034-14666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-71776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-34923.png)
解法二 因为a∥b,所以tanθ=2.所以 sinθ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034034-56283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034034-50783.png)
因此 sin2θ=2 sinθcosθ=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034032-27149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-71776.png)
所以sin(2θ+
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-80463.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-60534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034034-14666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-60534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034032-27149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034034-14666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034033-71776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034029-34923.png)
核心考点
试题【设向量a=(2,sinθ),b=(1,cosθ),θ为锐角(1)若a·b=,求sinθ+cosθ的值;(2)若a//b,求sin(2θ+)的值.】;主要考察你对平面向量数量积的意义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-51676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-96164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-52664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-36879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-96164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-40258.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-40258.png)
(2)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-76136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034021-40258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034022-58085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034022-80282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034022-77528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034022-86574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034013-90986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034004-62362.jpg)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034004-58364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034004-74388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034004-58364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034005-60088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034005-35504.png)
(2)若P为中线AM上的一个动点,求
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034005-33745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034005-20302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104034006-22978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-35332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-90869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-35332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-90869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-35332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-90869.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-35332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-92258.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-30973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033957-91831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033950-56040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033950-43902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033951-78466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104033951-49336.png)
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