1 . 对于函数
,其中
,
.
(1)求函数
的单调增区间;
(2)在锐角三角形
中,若
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3839dbbf132fc23661b92397964bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)在锐角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3c28e2fc237e76e757b8a82c619802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5021b03ffbc13e74ccd5fce3d6f43fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2024-04-11更新
|
683次组卷
|
3卷引用:上海市青浦区2024届高三下学期4月学业质量调研数学试卷
名校
2 . 已知复数
,其中
.
(1)设
,若
是纯虚数,求实数
的值;
(2)设
,分别记复数
、
在复平面上对应的点为
、
,求
与
的夹角以及
在
上的数量投影.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c0fda5d04e27796f64c5b3a09daa58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa44c6f189099dbe176aec25d1be094c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ea3cc01ce7266cdf0fd73fd50d23c8.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/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
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2024-03-12更新
|
589次组卷
|
2卷引用:上海交通大学附属中学2023-2024学年高二下学期摸底数学试卷
名校
解题方法
3 . 已知
是坐标原点,
,
(1)求向量
在
方向上的投影向量的坐标和数量投影;
(2)若
,
,
,请判断C、D、E三点是否共线,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1483e8351f585ca23025ec0c46f0a6e.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba0ea537c4145d273b81ada981ee3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4600168dd0570abb535b7c15af66ddf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b594e00f9aad4faf4907ec01f8112eb5.png)
您最近一年使用:0次
2023-04-27更新
|
797次组卷
|
2卷引用:上海市松江二中2022-2023学年高一下学期期中数学试题
名校
解题方法
4 . 如图,在扇形
中,
,半径
,
为弧
上一点,
是线段
上异于点
、
的一个动点.
(1)若
在
上的投影不小于2,求
的取值范围;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff5c21185c13eae675906dabd3593c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bf7d7fa347c09dedde116bb787a3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a046d7060dc843c78af806ee24f556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af18d542323baacfa180004c3449dc7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc7764d625d4c6c07e4946678cbee74.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
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名校
5 . 已知向量
,
,
(
),其中
为坐标原点,且
.
(1)若
,求
的值;
(2)若向量
在向量
方向上的数量投影为
,且
,求
的面积,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5fdc7cc778ba59d10aa6a607a62a6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bbcdda05263f5f3521698b54c3289d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08277b28ba242ce84a27c06dfcb9edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc05f40eb2357f219d31bd2ea8e785f7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4046de89a756c5347a80971cc2b2d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628560d39eeb0339fa00c9c15ab2c095.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a85504daf1129e372b3db4f704dbf8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
名校
6 . 我们可以利用向量知识求一些三角式的值.比如,在平面上有一边长为1的正五边形
,边长
与数轴l成
角,顶点A、B、C、D、E在数轴l上的垂直投影分别
.可以通过计算:
,
的值来计算
的值.大家可以通过上述提示,利用向量计算下面代数式的值:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36581140ebac5d28438ea63b1b23b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72414fd36f9f6b2c58a7380c6036fabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13c8af551c0d4f83a9069a52857ee92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c6bb02ba40b442af411fbb878c387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c04ae5c852a85d05522061be42e9ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87af3d7dae41121167bb3d4a9f72cbc5.png)
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2022-04-01更新
|
355次组卷
|
2卷引用:上海交通大学附属中学2021-2022学年高一下学期3月线上测试数学试题(2)
7 . 在
中,设
,记
的面积为
.
(1)求证:
;
(2)设
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59146c0725095d4bca6caa7b3357ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba2a1bf3e72ec2c2004495bc5a5aa68.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5a13ec22ea22408270baaaf4514eaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0066f0f0e650bc85331c4e3db945f4b5.png)
您最近一年使用:0次
20-21高一下·上海浦东新·阶段练习
名校
解题方法
8 . (1)请你利用数量积的定义(非坐标运算公式)证明:
;
(2)已知向量
与
的夹角为
,
,
,记
,
,若
,求实数k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4251b01d3a622638a54f4b839bacf95.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f18996bd00253c3ad9f91780103affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03ef3e7fb905b47f36c4630fcc65dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05dbf33b2c0984ee458fa9dc91ecf412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495af06bb4bfd6573b9a0ed151d03af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ee59964f020fc52b5ba66a3f5fcc3c.png)
您最近一年使用:0次
名校
9 . 已知函数
.
(1)求
的最大值;
(2)在
中,内角
、
、
所对的边分别为
、
、
,若
,
、
、
成等差数列,且
,求边
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d409a37d290aa5b2e6a512e3d315b1a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a30cdeccc312028502c30ca324d62e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ee0da554e49ecd3b5aa91551a23766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-06-04更新
|
669次组卷
|
4卷引用:2019年12月上海市松江区一模数学试题
2019年12月上海市松江区一模数学试题安徽省宿州市泗县第一中学2021届高三下学期最后一卷文科数学试题(已下线)考点14 三角恒等变换-备战2022年高考数学(文)一轮复习考点帮(已下线)专题12 平面向量-备战2022年高考数学学霸纠错(全国通用)
20-21高一下·浙江·期末
解题方法
10 . 已知函数
,点
,点
,和函数
图象上的点
.过B作直线
的垂线,垂足为Q.
![](https://img.xkw.com/dksih/QBM/2021/5/19/2724631972438016/2724654508531712/STEM/fb601df9-7d9b-4d94-ba40-cdd36dab4ddd.png)
(Ⅰ)若
,求
(最后结果用a表示);
(Ⅱ)若
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1a81492920894903aec53e797d8f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb30d60a5fd19a4064119f1991852a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab1eb15ebb7da16b52b95b6b69341f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b0ac6329573eca6908baecade254c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/2021/5/19/2724631972438016/2724654508531712/STEM/fb601df9-7d9b-4d94-ba40-cdd36dab4ddd.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31924857ab43b4e18367d50530ce6966.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7412b9f823b19b3fa63a7287c2214d.png)
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