题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-84101.png)
(1)将四边形ABCD的面积S表示为θ的函数;
(2)求S的最大值及此时θ角的值.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-31975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
(2)S取得最大值1+
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-31975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-10834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-62210.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-47487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-47487.png)
因为△BDC是正三角形,则S△BDC=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030416-89168.png)
由△ABD及余弦定理,可知BD2=12+12-2×1×1×cosθ=2-2cosθ,
于是四边形ABCD的面积S=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-47487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030416-89168.png)
即S=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-31975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
(2)由(1),知S=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-31975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
由0<θ<π,得-
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030416-38172.png)
故当θ-
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-10834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-31975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-27921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-10834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030415-62210.png)
核心考点
试题【如图所示,在四边形ABCD中,AB=AD=1,∠BAD=θ,而△BCD是正三角形.(1)将四边形ABCD的面积S表示为θ的函数;(2)求S的最大值及此时θ角的值】;主要考察你对解三角形应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030409-85785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030409-41360.png)
A.16 | B.![]() | C.18 | D.32 |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030356-93694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030356-67081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030356-93694.png)
A.![]() | B.![]() | C.1 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030343-64340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030343-39667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030337-95328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030337-85405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020030337-58483.png)
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