1 . 在
中,
,在斜边
与直角边
上各取点
,使得
,现沿着直线
将
进行翻折至
.
(1)证明:当
时,
;
(2)当三棱锥
的体积为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c963a0c412ca06827d633d28df409f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9b38b87305ec46c61aeb7554f29222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a4feb150ad9cff8d70431c97eb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd4d3653347116b65c45b57223f96e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/25/2cd81ef5-cdea-40b7-bf54-602ec7c94aca.png?resizew=292)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795d1f8e68aee16240a4018dcbcb1e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e403844f3bf87b4ebcdc4d28bbb04d.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17b7a10200a8e7b6ddcb375b0747107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5040d31e784398842b04ed7dd0aacc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452c39e9c252d158710c86a3263c9fe7.png)
您最近一年使用:0次
名校
解题方法
2 . 十字测天仪广泛应用于欧洲中世纪晚期的航海领域,主要用于测量太阳等星体的方位,便于船员确定位置.如图1所示,十字测天仪由杆AB和横档CD构成,并且E是CD的中点,横档与杆垂直并且可在杆上滑动.十字测天仪的使用方法如下:如图2,手持十字测天仪,使得眼睛可以从A点观察.滑动横档CD使得A,C在同一水平面上,并且眼睛恰好能观察到太阳,此时视线恰好经过点D,DE的影子恰好是AE.然后,通过测量AE的长度,可计算出视线和水平面的夹角
(称为太阳高度角),最后通过查阅地图来确定船员所在的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/f340736c-a23f-4b3e-a3ef-710244b4e922.png?resizew=359)
(1)若在某次测量中,横档
的长度为20,测得太阳高度角
,求影子AE的长;
(2)若在另一次测量中,
,横档
的长度为20,求太阳高度角的正弦值;
(3)在杆AB上有两点
,
满足
.当横档CD的中点E位于
时,记太阳高度角为
,其中
,
都是锐角.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5157b42da58d55daad27d98b2fec15ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/f340736c-a23f-4b3e-a3ef-710244b4e922.png?resizew=359)
(1)若在某次测量中,横档
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b528818e98c5c2ddf301048b4228d2.png)
(2)若在另一次测量中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e847821c95966efc534f26fbe4f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)在杆AB上有两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2059d1b10017e04aa35812c0354049b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafc046509e3ca71090d8a1de862efa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadb2357b7a648d3a69c7a84dbdffcc0.png)
您最近一年使用:0次
2023-04-26更新
|
1485次组卷
|
6卷引用:四川省德阳市德阳中学校2022-2023学年高一下学期5月月考数学试题
名校
解题方法
3 . 已知
为奇函数.
(1)求
的值;
(2)若
,
,求
的值;
(3)当
时,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91c52724c5ab0d36c22d84e1670caf7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da256819b7a7f15c1c1ae32c3b8c9193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96119cc3005adf559140161bd872143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6c487eb2719ca41ee5ab54701e29b3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cf9c12181dd8683944b2b30bf8e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4a4cfb52d401764105135cd21d6568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbc4174e43957bd666d2467faced6e2.png)
您最近一年使用:0次
2022-06-14更新
|
1102次组卷
|
3卷引用:四川省德阳市2020-2021学年高一下学期期末数学试题
4 . 已知直线
与函数
,
的图象均相切,切点分别为
,
.
(1)当直线
的斜率为
时,求
的值;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7c4adef3485e8ac6e50d1926365327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5fd5c03661b5632ad824eea4b8b75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
(1)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0d0a4ef6099abc11733e718be8833f.png)
您最近一年使用:0次
2021-10-03更新
|
264次组卷
|
2卷引用:四川省德阳市第三中学2022-2023学年高三上学期第一次综合考试(开学考试)数学试题