题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043149-13307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043149-42835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043150-55104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043150-76914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043150-62835.png)
(Ⅰ)求角A的大小;
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043150-46730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043149-13307.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-10322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-87385.png)
解析
试题分析:(Ⅰ)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-37437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-91490.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-87345.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043152-83731.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043152-74840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043152-52449.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043152-56989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043153-40012.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043153-61143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043153-18101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-10322.png)
(Ⅱ)由余弦定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043153-84559.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043153-50454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043154-47817.png)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043154-78789.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043149-13307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043154-79790.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043149-13307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043151-87385.png)
点评:三角函数的图象和性质是高考中必考的内容,此外二倍角公式、辅助角公式和正弦定理和余弦定理经常综合考查.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043141-85433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043141-60721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043141-64090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043141-96547.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043141-73174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043142-59294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043142-37200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043142-52555.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043141-96547.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043142-57809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043143-88122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043143-63081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043143-39611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043134-62174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043134-25210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043134-19835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043134-83270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043134-42632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043134-18594.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043135-51798.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043135-33122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043129-14144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043129-34371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043129-84446.png)
一艘轮船按照北偏西50°的方向,以15海里每小时的速度航行,一个灯塔M原来在轮船的北偏东10°方向上,经过40分钟,轮船与灯塔的距离是
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043125-66926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043125-34599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043117-77357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043117-96403.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043117-91864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043117-69916.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043117-14706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043118-98784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043118-20719.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043118-90160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043118-47030.png)
④若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043118-12378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043119-14289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020043119-19153.png)
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