真题
1 . 如图,平面四边形ABCD中,
,
,
,
,
,点E,F满足
,
,将
沿EF翻折至
,使得
.
;
(2)求平面PCD与平面PBF所成的二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9335f4d4bb04e45cd7bc8da52f694f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eac9b73cc6c95e0aa7dcf354bb3c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed47dc5be420ecae1e068cd889b38256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b198dacba184a1b6adf6f0cf2b3d76fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11917085059a83ae9771e6712a2a1cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218870b4b09ddcb96183d6f9c672fb70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7459863f058993e17b7dcf902053eccd.png)
(2)求平面PCD与平面PBF所成的二面角的正弦值.
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6卷引用:2024年新课标全国Ⅱ卷数学真题
2024年新课标全国Ⅱ卷数学真题(已下线)2024年高考数学真题完全解读(新高考Ⅱ卷)专题07立体几何与空间向量(已下线)2024年新课标全国Ⅱ卷数学真题变式题16-19(已下线)五年新高考专题07立体几何与空间向量(已下线)三年新高考专题07立体几何与空间向量
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2 . 如图,在四棱锥
中,平面
⊥平面
,
为等边三角形,
,
,
,
,M为
的中点.
⊥平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77dd36d86b0f066b437e5ffec67110ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
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2024-06-05更新
|
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5卷引用:2024届山东省威海市高考二模数学试题
2024届山东省威海市高考二模数学试题(已下线)第五套 艺体生新高考全真模拟 (二模重组卷)(已下线)湖南省益阳市2024届高三下学期5月适应性考试数学试题广东省江门市鹤山市第一中学2023-2024学年高二下学期第二阶段考试(5月)数学试题江苏省海门中学2023-2024学年高二下学期5月学情调研数学试卷
3 . 如图,在多面体
中,四边形
为菱形,平面
平面
,平面
平面
是等腰直角三角形,且
.
平面
;
(2)若
,求平面
与平面
所成锐二面角的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0e7e1ea69f9f455e8496304b6a30c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde1e200d1dd5ddc433c876c9d2f688c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db74cdd38ce73c5631cad19c1f39804.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76474dae014dc19bcbe7c1919a6d3044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d98d25467d8a11ddeeb1e6e18eb704f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fffcd1e524b0c7ef79f84384817293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
您最近一年使用:0次
2024-06-03更新
|
710次组卷
|
4卷引用:四川省眉山市2024届高三下学期第三次诊断考试理科数学试题
四川省眉山市2024届高三下学期第三次诊断考试理科数学试题(已下线)第4套 新高考全真模拟卷(三模重组)(已下线)易错点4 忽视法向量夹角与二面角的关系四川省雅安市神州天立学校2024届高三高考适应性考试(三)数学(理)试题
2024·全国·模拟预测
4 . 如图,三棱锥
中,
,
,
,平面
平面
分别为棱
的中点.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618aaecadee80a640c0019db0e9e2ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0595498034037b58538f8056dbc6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf42acb8d1875acf1775e30ae2e3d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12fa54e80fc52de0701cddc9a4ed47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbb19cb4eb2d7f3207559eb07355ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13259de331de43dda25f2688b7822663.png)
您最近一年使用:0次
5 . 如图,多面体
中,
和
均为等边三角形,平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0b4b072ebf21f947fddc1b70554ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
;
(2)求平面ABD与平面PBC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1e3a43d0fa18f6c0888ba804d5b329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73636989e83905f8800a865c2b608c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0b4b072ebf21f947fddc1b70554ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求平面ABD与平面PBC夹角的余弦值.
您最近一年使用:0次
解题方法
6 . 在正方体
中,点M为线段
上的动点(含端点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.存在点M,使得![]() ![]() |
B.存在点M,使得![]() ![]() |
C.不存在点M,使得直线![]() ![]() ![]() |
D.不存在点M,使得直线![]() ![]() ![]() |
您最近一年使用:0次
2024·全国·模拟预测
7 . 在四棱锥
中,底面
为矩形,点
为
的中点,且
.
.
(2)若
,点
为棱
上一点,平面
与平面
所成锐二面角的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c807097a923a5a7c72c7e32b259654e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9425630dcfe5a824c44904d4f71e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcd55ad87acd31ce56136e0c11ed300.png)
您最近一年使用:0次
8 . 已知四棱锥
中,底面
是矩形,
,
.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b51401875599d32a2ec41b70ac75e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae4011a59f40f68793bb41a7982b93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d07f36efcb9d203267d7c0409720cf.png)
您最近一年使用:0次
2024-04-26更新
|
1737次组卷
|
3卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
2024·全国·模拟预测
9 . 如图,多面体
中,四边形
是正方形,四边形
为直角梯形,
,
,
,
为
上一点,且
.
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a685fd7539b94dcede33055ef3b0e340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02b1139e07e431b5d4276757b232bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6bcf7a81baf90480b616b9a5fde3493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f723850c512ee4df6ea48ff2c38ff6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c16aa31938679a9ee9686ae46409b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cdec00111d2d349c34dd63184c752b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/335187895f612ce811414cfbedf89467.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea525564975bca3c35b6ca1d89e0cd40.png)
您最近一年使用:0次
解题方法
10 . 如图,正方体
中,P是线段
上的动点,有下列四个说法:
①存在点P,使得
平面
;
②对于任意点P,四棱锥
体积为定值;
③存在点P,使得
平面
;
④对于任意点P,
都是锐角三角形.
其中,不正确 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
①存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0875cc63101ea9c8a7ad19a94bd6d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4525d2a5cfdd4c82f62c28177d6cf9.png)
②对于任意点P,四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6d814d90e9b96940905db241063a5c.png)
③存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74827ace228023ae8bdf649a4517c3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957a3d3c306dfb26ac61c9cbf519622e.png)
④对于任意点P,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd5683dba7d9f29d643e9a3e3204fa8.png)
其中,
A.① | B.② | C.③ | D.④ |
您最近一年使用:0次