解题方法
1 . 如图,在四棱锥
中,
底面
,
,
,
,
,点E为棱
的中点.证明:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/c4edf5eb-4db7-4591-932a-0e5afa7dcbc6.png?resizew=197)
(1)
平面
;
(2)平面
平面
;
(3)求平面
与平面
所成角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba814113887c21637c1954f244812f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/c4edf5eb-4db7-4591-932a-0e5afa7dcbc6.png?resizew=197)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7609a1407f1e965fc9f1235552dcf9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3142b1af4ce67d3e55417b4c0de257.png)
您最近一年使用:0次
2 . 如图
为直三棱柱,
,
,设
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/614f9a67-f2f0-493a-8c27-de4544365149.png?resizew=152)
(1)证明
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46720eabe78e309e02c24678632b586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/614f9a67-f2f0-493a-8c27-de4544365149.png?resizew=152)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8a2f9862ddd955ab46721ff764f2ec.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
您最近一年使用:0次
2024-01-25更新
|
110次组卷
|
2卷引用:四川省广元市川师大万达中学2023-2024学年高二下学期入学考试数学试题
名校
解题方法
3 . 在梯形
中,
,
,
,P为
的中点,线段
与
交于O点(如图1).将
沿
折起到
位置,使得平面
平面
(如图2).
(1)求二面角
的余弦值;
(2)线段
上是否存在点Q,使得
与平面
所成角的正弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d185e7050dcf0d8c3a5532e44c68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89ee6576c35c682bcb0eff43bd958d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6829c6214e60edbfbf1e31601c6bcb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb3c5eea67eecdd13a2e6cd60d1d67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49d869110f27140f5c1934143db2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/23/f244259e-2eba-4ebc-aa76-04ea521db43b.png?resizew=458)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3036d3535c0bdccd19039cf1962218ce.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be451ce5fad246389ccf4864929d81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e95fa1c3bcd3d0464fcadf248e90ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80dbac2006d30c49943f0241fd976eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b188172a322d69106c638e1603ac13f.png)
您最近一年使用:0次
2023-11-02更新
|
3451次组卷
|
7卷引用:四川省广元市苍溪中学校2023-2024学年高二上学期12月月考数学试题
名校
解题方法
4 . 如图,在四棱锥
中,底面ABCD为菱形,
,
,E为棱AB的中点.
(1)证明:平面
平面ABCD;
(2)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8a1ea8fca7c80a86dbe4d85cf9707d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/22/90263287-425a-4b62-8735-edbb61a466c0.png?resizew=172)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f6967901d6c855864df01e7bf7a15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abca0f7f7f2f49d821be607579565963.png)
您最近一年使用:0次
名校
5 . 在直角梯形
中,
,
,
,直角梯形
绕直角边
旋转一周得到如下图的圆台
,已知点
分别在线段
上,二面角
的大小为
.
(1)若
,
,
,证明:
平面
;
(2)若
,点
为
上的动点,点
为
的中点,求
与平面
所成最大角的正切值,并求此时二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee581a35a1906bb22d3c85f0347821c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad16665c5d47ce756cc2980423bf4b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f514087cda61f4e72fb4a709c03316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17230625e72d3a9c6d72ff61019ff61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9944f447c7635d82dee5d5eb26994dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb58df55d96d15e4d66a983964efaba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/6/b4e5e52f-f943-4c1f-80af-c7449e473146.png?resizew=170)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92723ed3e62865396c01531eba603a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31517a881a9e728adf27688b0fb6bcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5b0adb655532ef12b711707e2b9e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e01739fdd26c48a30257999ce449ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5247cb4bcf395152043841f784722a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2403e37c7f9abc596ce2452e3722607.png)
您最近一年使用:0次
2023-06-02更新
|
1101次组卷
|
8卷引用:四川省广元中学2023-2024学年高二上学期第一次阶段性测试(10月)数学试题
名校
解题方法
6 . 在平行四边形ABCD中,
,
,
,过D点作
于E,以DE为轴,将
向上翻折使平面
平面BCDE,连接CE,F点为线段CE的中点,Q为线段AC上一点.
(1)证明:
;
(2)若二面角
的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6834ac70927ae08d7d36a1922403c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13c772461aef1d9d715129636739748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/28/cf5629b1-8541-4901-b46c-977acf226849.png?resizew=322)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2a245381e615882ee5feb7793a1df6.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfe02a5d85618884803e98257922c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bbc95a59f754acf111bcba7cd14c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe5e47c1cfe0d419bacbba32851ed71.png)
您最近一年使用:0次
2023-05-26更新
|
925次组卷
|
3卷引用:四川省广元市宝轮中学2023届高三仿真考试(二)数学(理)试题
名校
7 . 如图,在四棱锥
中,底面ABCD为矩形,
平面ABCD,M为PC中点.
平面MBD;
(2)若
,求直线BM与平面AMD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337f017d0c8eeb3f181e0211935ecf2d.png)
您最近一年使用:0次
2023-04-14更新
|
1784次组卷
|
8卷引用:四川省广元中学2023-2024学年高二上学期第一次阶段性测试(10月)数学试题
名校
解题方法
8 . 如图,四棱锥P-ABCD,平面PAB⊥平面ABCD,PA⊥AB,
,∠DAB=90°,PA=AD,DC=2AB,E为PC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/e08ff188-5d12-4282-806e-4a1d8a420234.png?resizew=167)
(1)求证:直线
//平面PAD;
(2)当AP=AB时,求平面PAD与平面PBC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/e08ff188-5d12-4282-806e-4a1d8a420234.png?resizew=167)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
(2)当AP=AB时,求平面PAD与平面PBC所成锐二面角的余弦值.
您最近一年使用:0次
2023-02-19更新
|
237次组卷
|
3卷引用:四川省广元市2022-2023学年高二上学期期末数学(理科)试题
名校
9 . 如图,在四棱锥
中,点
都在以
为直径的圆上,
平面
,M为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/371c174f-be1b-4e11-934e-f072e6900821.png?resizew=160)
(1)证明:
平面
;
(2)若
是正三角形,
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/371c174f-be1b-4e11-934e-f072e6900821.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2414af3e0d759c372dc805110ca87fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f239fbcc58fc15535db4b5084c4f7253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-01-19更新
|
302次组卷
|
3卷引用:四川省剑阁中学校2022-2023学年高二下学期第一次质量检测理科数学试题
11-12高二上·福建·期末
10 . 如图,在长方体
中,
,
,点E在棱AB上移动.
;
(2)当点E为棱AB的中点时,求点E到平面
的距离;
(3)当AE为何值时,平面
与平面
所成的角为
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa81c1f81266b4ef3d471bc6bfc38d.png)
(2)当点E为棱AB的中点时,求点E到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(3)当AE为何值时,平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb4e4c148b9185e09e454955eaa7312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
您最近一年使用:0次
2022-03-05更新
|
749次组卷
|
9卷引用:2014-2015学年四川省广元实验中学高二下学期期中考试理科数学试卷
2014-2015学年四川省广元实验中学高二下学期期中考试理科数学试卷(已下线)2011年福建师大附中高二第一学期期末数学理卷(已下线)2012届新人教版高三上学期单元测试(6)数学试卷(已下线)2013届天津市高考压轴卷理科数学试卷2015-2016学年天津市一中高二上学期期中理科数学试卷(已下线)复习题二4江苏省盐城市伍佑中学2021-2022学年高二下学期第一次阶段考试数学试题2005年普通高等学校招生考试数学(理)试题(江西卷)湘教版(2019)选择性必修第二册课本习题第2章复习题