1 . 判断正误(正确的写正确,错误的写错误)
(1)对任意角
,
都成立.( )
(2)对任意角
,
都成立.( )
(3)存在角
有
.( )
(4)若
,则
的值一定有二个.( )
(1)对任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6ac117b36013ac6ba9e5588c390102.png)
(2)对任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c815b129e14f69e92ab9a4b03412acfc.png)
(3)存在角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcb897d54e85c8bc3ba4b795a968518.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28210eadef3311933aa0b676c81cbd8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66db91bb3be9e2b6ad567774e3699758.png)
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2 . 为了推导两角和与差的三角函数公式,某同学设计了一种证明方法:在直角梯形ABCD中,
,
,点E为BC上一点,且
,过点D作
于点F,设
,
.
(1)利用图中边长关系
,证明:
;
![](https://img.xkw.com/dksih/QBM/2023/6/20/3263775491006464/3265425842176000/STEM/d80ec35b6b4c44ad9d54317146a5675c.png?resizew=47)
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d8397018b0a01a1b4e9574604f9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5427b7b994b860628df3d6b7a07de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa30a9ee227af2b387cf6e028c20d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a447d8fc6919edd758ccec4277435aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21461e9cb1265843a16d379788f3fcb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/24/b7c91a13-25b3-41d4-9180-c25f2539ec0f.png?resizew=133)
(1)利用图中边长关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8904ac51eff2df308ed7b6a07aa2477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8b8ee28cf91c5976d074d233c941f3.png)
![](https://img.xkw.com/dksih/QBM/2023/6/20/3263775491006464/3265425842176000/STEM/d80ec35b6b4c44ad9d54317146a5675c.png?resizew=47)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952ab659a747b410974aa88748f18d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fff423fa9846e49124710a2add054a8f.png)
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名校
解题方法
3 . 古希腊数学家阿波罗尼斯采用平面切割圆锥面的方法来研究圆锥曲线,如图1,设圆锥轴截面的顶角为
,用一个平面
去截该圆锥面,随着圆锥的轴和
所成角
的变化,截得的曲线的形状也不同.据研究,曲线的离心率为
,比如,当
时,
,此时截得的曲线是抛物线.如图2,在底面半径为
,高为
的圆锥
中,
、
是底面圆
上互相垂直的直径,
是母线
上一点,
,平面
截该圆锥面所得的曲线的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/9/011f64b8-0f83-457b-8f87-5174f47d8bce.png?resizew=143)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/1441e670-fcd8-48fb-a66c-daa471c37e98.png?resizew=176)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dd0c52aca1675c17b9a019aa7901e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e55f4e5a5d84670bbf3de150da74b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dbcaa127022fbd6b6f13345196408a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3358e5017bb8701143245ad5a1568219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/9/011f64b8-0f83-457b-8f87-5174f47d8bce.png?resizew=143)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/1441e670-fcd8-48fb-a66c-daa471c37e98.png?resizew=176)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-06更新
|
1078次组卷
|
5卷引用:贵州省贵阳市2023届高三适应性考试(二)数学(理)试题
解题方法
4 . 下列说法中正确的有( )
A.若![]() ![]() |
B.已知角![]() ![]() ![]() |
C.已知角![]() ![]() ![]() |
D.对于任意角![]() ![]() |
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解题方法
5 . 从下面①②③中选取一个作为条件,完成所给的两个问题.
①
②
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbe6cf5b3536475beb854b1cb5173d3.png)
(1)求
的值;
(2)若
,求
的值.
注:若选择多个条件分别解答,则按第一个解答计分.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be602250a0bbf24f1ca78b406bc1fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c02e3d360e5e6ab98744fbb4f900c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbe6cf5b3536475beb854b1cb5173d3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58da07493c8cf02e78239d815922329a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c87874458fabe50aff5e19d586d5d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1830cf41733a28d7b708ef64df7b242.png)
注:若选择多个条件分别解答,则按第一个解答计分.
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解题方法
6 . 已知
,
,且
,下面选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/867615f26578c7d01c3e484d39c4996a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023aa2bc1555f043aba66da1687b1e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff6dcc389a1f5d6cf1d877168ad157f.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
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7 . 知道在直角三角形中,一个锐角的大小与两条边长的比值相互唯一确定,因此边长与角的大小之间可以相互转化.与之类似,可以在等腰三角形中建立边角之间的联系,我们定义:等腰三角形中底边与腰的比叫做顶角的正对
.如图,在
中,
.顶角
的正对记作
,这时
.容易知道一个角的大小与这个角的正对值也是相互唯一确定的.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/5b08a58e-a870-4476-94b0-748fead6aa54.png?resizew=112)
根据上述对角的正对定义,解下列问题:
(1)
的值为( )
A.
B.
C.
D.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)对于
,
的正对值
的取值范围是______.
(3)已知
,其中
为锐角,试求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab3e912f74f80b0878f90c88d42af80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf41b94bb22f385601fa21c3cf435470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea36188262b6bbf9098ba084b1d66bc8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/5b08a58e-a870-4476-94b0-748fead6aa54.png?resizew=112)
根据上述对角的正对定义,解下列问题:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d9d97b81f939119268d8006bedac0a.png)
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a54e7d6e547a5d4850edc4025eeacc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73738e78a4d8e6df0129113ada99f4fc.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bc052a11cf1a01445992672dde2836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4777985fe308c220d5827aae7b93f4c.png)
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名校
解题方法
8 . 下列命题中正确的有( )
A.![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.圆心角为![]() ![]() ![]() |
您最近一年使用:0次
2022-12-13更新
|
752次组卷
|
4卷引用:1.4.2单位圆与正弦函数、余弦函数的基本性质(课件+练习)
(已下线)1.4.2单位圆与正弦函数、余弦函数的基本性质(课件+练习)四川省成都市新都区新都香城中学2022-2023学年高一上学期期末数学试题广东省河源市龙川县第一中学2022-2023学年高一下学期期中数学试题湖南省邵阳市新邵县第八中学2021-2022学年高一上学期选科调研考试数学试题
解题方法
9 . 文笔塔,又称慈云塔,位于保山市隆阳区太保山麓,古塔建设于唐代南诏时期.2007年4月在原址拆除重建后的文笔塔新塔与广大市民见面.如图,某同学在测量塔高AB时,选取与塔底在同一水平面内的两个测量基点C和D. 测得
,在点 C测得塔顶A仰角为
,已知
,
,且CD=56米.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/67e9e8e1-fd71-4887-95b0-b443df498c81.png?resizew=186)
(1)求
;
(2)求塔高AB(结果保留整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121267ef1c4996ffba5c6eb46d4cd1dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562db28cd1606605a3418c89c2d69465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d97c1920488faf1148ed87c25bfc3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/31/67e9e8e1-fd71-4887-95b0-b443df498c81.png?resizew=186)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4fe85ca088b8de0784f105f3cbec6f.png)
(2)求塔高AB(结果保留整数).
您最近一年使用:0次
2022-07-20更新
|
1009次组卷
|
4卷引用:6.4.3 课时3 余弦定理、正弦定理应用举例(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)
(已下线)6.4.3 课时3 余弦定理、正弦定理应用举例(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)高考新题型-平面向量及其应用(已下线)第12讲 余弦定理、正弦定理的应用云南省保山市2021-2022学年高一下学期期末质量监测数学试题
10 . 如图, 椭圆
的右焦点为
,过点
的一动直线
绕点
转动,并且交椭圆于
两点,
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2022/6/17/3003466465910784/3006188991668224/STEM/aebf6761b71240a6943db93c8219b518.png?resizew=333)
(1)求点
的轨迹
的方程;
(2)在
的方程中, 令
,
.
①设轨迹
的最高点和最低点分别为
和
,当
为何值时,
为正三角形?
②确定
的值, 使原点距直线
最远, 此时, 设
与
轴交点为
,当直线
绕点
转动到什么位置时,
的面积最大, 并求出面积的最大值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b77a34ceb387940caecbe9cb1d5dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1e2b23e8994b2960affe9efccd622b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2022/6/17/3003466465910784/3006188991668224/STEM/aebf6761b71240a6943db93c8219b518.png?resizew=333)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e598f08618337323f0ca508a99c4331c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9466e23ac5c00b30ea5517b144ce44f.png)
①设轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
②确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea69edc95ed3445574e0272896b3d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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