解题方法
1 . 球面几何在研究球体定位等问题有重要的基础作用.球面上的线是弯曲的,不存在直线,连接球面上任意两点有无数条曲线,它们长短不一,其中这两点在球面上的最短路径的长度称为两点间的球面距离.
纬线,赤道以北叫做北纬.如图1,将地球看作球体,假设地球半径为
,球心为
,北纬
的纬线所形成的圆设为圆
,且
是圆
的直径,球面被经过球心
和点
,
的平面截得的圆设为圆
,求圆
中劣弧
的长度,并判断其是否是
,
两点间的球面距离(只需判断、无需证明).
(2)如图2,点
,
在球心为
的球面上,且
不是球的直径,试问
,
两点间的球面距离所在的圆弧
是否与球心
共面?若是,写出证明过程,并求出当
,
时,
,
两点间球面距离所在的圆弧
与球心
所形成的扇形
的面积;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d495d88b8e51f89e2e4da27328025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240d929040e21e7991481149b73a79a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
(2)如图2,点
![](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/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93ef48e154646ef0564de14a990c2e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c467c10aa2eabce3af68c1213d88043b.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/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c880639a6164aa127cf38b63aebde50.png)
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解题方法
2 . 如图所示是某斜拉式大桥图片,为了解桥的一些结构情况,学校数学兴趣小组将大桥的结构进行了简化,取其部分可抽象成图(1)所示的模型,其中桥塔
与桥面
垂直,通过测量得知
,当
为
中点时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/8eb65219-6da9-485d-9251-edfc6794b1eb.png?resizew=383)
(1)求
的长;
(2)设
,写出
与
的函数关系式;
(3)已知命题:函数
在
内为严格增函数;求证该命题为真命题,并用该命题求解
在线段
的何处时,
达到最大,最大值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947a9e717f8bd9e2f5eb3ba8929932a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a3caf9045a08a8342c73496c4274cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1d0963bbe4d4d8eda2210585fc1d7d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/8eb65219-6da9-485d-9251-edfc6794b1eb.png?resizew=383)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd459a6de5d294b1dfb95e596793f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)已知命题:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a869a76555f3369728f9005863bdb8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf1667b21a273bf5dd007d65eeda7c.png)
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2023-03-30更新
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3卷引用:上海市金山中学2022-2023学年高一下学期3月素养检测(一)数学试题
上海市金山中学2022-2023学年高一下学期3月素养检测(一)数学试题上海市奉贤中学2022-2023学年高一下学期期中数学试题(已下线)专题12 寒假成果评价卷 -【寒假自学课】(沪教版2020)