解题方法
1 . 如图,在正三棱柱
中,
分别是
的中点.
为矩形
内动点,使得
面
,求线段
的最小值;
(2)求证:
面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0f13ea92fd3d07ff1d80d2525ed904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63646644bdc10fe8a669a61c592c8b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfed58659a9cab4d1836c3d2effdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9383df25a7d6d69d470086f54d525e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877bda7e850ca4a33e517fcf4a082b42.png)
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解题方法
2 . 已知
分别为锐角三角形
三个内角
的对边,且
.
(1)求
;
(2)若
,
为
的中点,求中线
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c976d105c27de505f83e7e40da698b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3ac959ebcb005ec9ebaff52f4ac70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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3卷引用:湖北省新高考联考协作体2023-2024学年高一下学期5月联考数学试题
湖北省新高考联考协作体2023-2024学年高一下学期5月联考数学试题(已下线)专题05 解三角形大题常考题型归类-期期末考点大串讲(人教B版2019必修第四册)云南省大理市2023-2024学年高一下学期6月质量检测数学试题
3 . 对于两条不同直线m,n和两个不同平面
,以下结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
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4 . 在
中,角A,B,C所对的边分别为
已知
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24159e05561cd9eeb073ff0438789d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知
是虚数单位,复数
,则复数
的虚部为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384849588f3e67d7da22738b08ca2b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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6 . 已知集合
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b1b758fc3341e9982556804a41b07c.png)
A.![]() | B.![]() | C.![]() | D.![]() ![]() |
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7 . 用平行于棱锥底面的平面去截棱锥,把底面和截面之间的那部分多面体叫做棱台.在正三棱台
中,侧棱
,则侧棱
与底面ABC所成角的正弦值为_____________ ,该三棱台的体积为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944f00d2d962252c286827fd47b4b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
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名校
解题方法
8 . 已知复数
(
为虚数单位).
(1)求
;
(2)若
,其中
,求
的值;
(3)若
,且
是纯虚数,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6275aab78ba9acf5242af47407f5bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949640658f3eb28025dc5ead55bcdea8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c05c638fa6ec40017a00a29bcc8bad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f844a74a4a9a02d6360b6384ebc4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1842a4178f1de5839194ff3134e13f2f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe3cb7e0694744d1e8a592592931642.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26dd5edae8097274a8a4fd56bc1b4c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
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解题方法
9 . 已知向量
,向量
与向量
的夹角为
.
(1)求
的值.
(2)若
,求实数
的值.
(3)在(2)的条件下,求向量
在向量
方向上的投影向量的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6d915a3019f08498f59037b342f421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8addbfcc46330524fdc9fd4f1532ab5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)在(2)的条件下,求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
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10 . 如图所示,圆内接四边形
中,
,
为圆周上一动点,
.
(2)若
,求AC的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c63bfe8427f7e8239bb3b11bd660f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df793f5dac174bc71bd1e82bbf5732b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b390d05e64fcf668472db4c1c51a1bf.png)
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