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1 . 在
中,角
对应的边分别为
,已知
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d12de0fe32eedb8fab4fd3a50dfa7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2bc8adc993cad5553d66285b5971f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 赵爽是我国古代数学家,大约在公元222年,他为《周髀算经》一书作序时,介绍了“勾股圆方图”,亦称“赵爽弦图”.(以弦为边长得到的正方形由4个全等的直角三角形再加上中间的一个小正方形组成,如图①),类比“赵爽弦图”,可构造如图②所示的图形,它是由3个全等的三角形与中间一个小等边三角形拼成的一个较大的等边三角形,其中
,则
的值为______ ;设
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bbe0491dc037390ef465b4deef4a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1412e959d8e97ae6bee534a319662e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e507d3941363e9dbeac8be35134727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
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3 . 已知点
,点
为原点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d54bcff5ffecbd3e4dea284d273638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8840adf41cb679f98b8bcb81ef4afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8731c539ba9ecf87f2fd501b77fbef.png)
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4卷引用:江苏省连云港市海州高级中学2023-2024学年高一下学期期中学情调查考试数学试题
4 . 复平面上两个点
,
分别对应两个复数
,
,它们满足下列两个条件:①
;②两点
,
连线的中点对应的复数为
,若
为坐标原点,则
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4158443ff179d0a71c63e762b502bb6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb8477bcc87b1401970171bf57b9ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1fd680a5d355178273c6d6025eb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c342b4049af5e211c8552e6f1d3526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91fcd06e9139169f341447eaf9617a4.png)
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5 . 在
中,内角
,
,
所对的边分别为
,
,
,若
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf7e2bd3d020fb7394e0988fa4af6b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5830bf026e686d59ae1a774f7e44074f.png)
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4卷引用:江苏省连云港市新海高级中学2023-2024学年高一下学期期中考试数学试卷
江苏省连云港市新海高级中学2023-2024学年高一下学期期中考试数学试卷湖北省黄冈市浠水县第一中学2023-2024学年高一下学期期末质量检测数学试题(已下线)专题4 解三角形中的最值与范围问题【练】(高一期末压轴专项)(已下线)【高一模块一】难度3 小题强化限时晋级练(基础3)
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6 . 如图,在扇形AOB中,
,
,点C在扇形AOB内部,
,
,则阴影部分的面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8ea58dc45bf719fa679db2ffa8a9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451156790ac81457a25bdfa06d867233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0590b80055f283b90bac195d99ccd44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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7 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f959c676ab8f896d6a2fae23dddaf90d.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bc052a11cf1a01445992672dde2836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f959c676ab8f896d6a2fae23dddaf90d.png)
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8 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f27f930806d4ee1a6ac77a0fa6c340.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c9df49c32fa5cfd53197f65e1af42a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f27f930806d4ee1a6ac77a0fa6c340.png)
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9 . 已知
,
是第四象限角,则
的值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57444ead804245890b18f4b8a2b4e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87a846fe363e4ae184c75f759b29c75.png)
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10 . 角
的终边上有一点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b80751c98f9991b9cfc03923a98834.png)
_______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90acecacaab778257a1a1e903b2028a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b80751c98f9991b9cfc03923a98834.png)
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