题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073935-71092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073935-36531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-56208.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-25267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-63978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-75984.png)
答案
解析
试题分析:(1)由扇形周长为定值可得半径与弧长关系
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-32496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073937-22117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073937-41427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073937-68190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073937-20869.png)
试题解析:(1)证明:设弧长为
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073937-87284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073938-36986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-32496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073938-83367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073938-58553.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073938-10947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073938-30354.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073938-63226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073939-35333.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-56208.png)
(2)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073939-25602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073939-23761.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-92206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-27676.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-47884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-54627.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-92206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-45279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-98824.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-75984.png)
法二:
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073941-36850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073941-72978.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073941-84266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073940-92206.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073941-46981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073941-44071.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073942-20798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073942-93190.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073942-59338.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073936-75984.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073933-27771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073933-25813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073933-27771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073934-27651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073930-24189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073930-72450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073930-18396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073927-42597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073927-79918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073925-60635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073925-36961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073926-75747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073926-62791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073920-97528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073920-28818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073920-53589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073921-52143.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073920-28818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073920-53589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073921-89413.png)
(2)已知角
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073921-80679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073921-37564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073922-26160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073922-22738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073922-18021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190821/20190821073922-12141.png)
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