1 . 定义运算“
”满足:
为从向量
按逆时针方向到向量
的夹角
,向量
垂直于
所确定的平面,当
时,其垂直平面的方向向上;当
时,其垂直平面的方向向下,下列说法一定正确的有__________ .(填序号)
①
;②
;③
;④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872c64b1cc0dd66a0d4f4bb437d6d50b.png)
;⑤当
时,
;⑥
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad8d792188dba9a934ff4e034e6eedd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3dfb49ad8bb91cc8a7488ff6f2b48d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2624a5cff11216693d7ecc7a8661c945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18020f8f5d3ec9988d05d367b9858fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c82ef71de70fda2db4b882e57bacbb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef7b23414e09377caa0d7fe2e6a5dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932413ffae6ac40f704ef9606bdc06a8.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a5dd9c18ec68a4e1af7a86abb44d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f57826c118e5772513c03354d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17be5a6799ad26c91a8fd58448a3ce03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872c64b1cc0dd66a0d4f4bb437d6d50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea925583bb5b08798bf5c0f9f43aad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b958a367fa2f08b6202a5a6ebf5e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d94b1db1042e2b0dbe7efb3a6e33190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fb176d7f8f34762a45717df116878ed.png)
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真题
2 . 设函数
的图象与直线
,
及
轴所围成图形的面积称为函数
在
上的面积,已知函数
在
上的面积为
.
(1)
在
上的面积为______ ;
(2)
在
上的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b334dafda377c3db77647c8cf1e95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e971b8f69f495694f7c6cddb527ec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5df66f4be5f7e0b424cff99b4616d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50673b4ba3c120bceb8bb8d0750bcf98.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49866c49c5c4f28bb783162076b8fff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e5257c3efa20386fa295fa96819200.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f751602f38272408dca8990fa8d4440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e5f0834f9e45e4b622d575f36dd7c2.png)
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2013·黑龙江齐齐哈尔·二模
名校
解题方法
3 . 定义运算:
,将函数
的图象向左平移
的单位后,所得图象关于
轴对称,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4402623f6364a12571fec757adce6b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f983b9005cf72faa198a3373583383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f07948e9258b482a2164ac871f90f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-09-12更新
|
1364次组卷
|
14卷引用:2013届黑龙江省齐齐哈尔市高三二模文科数学试卷
(已下线)2013届黑龙江省齐齐哈尔市高三二模文科数学试卷【全国百强校】贵州省凯里市第一中学2018届高三下学期《黄金卷》第四套模拟考试数学(理)试题(已下线)河北省衡水中学2019届高三年级六调考试理科数学试题(已下线)2020届高三12月第02期(考点04)(文科)-《新题速递·数学》河北省衡水中学2019届高三下学期六调数学(理)试题2020届陕西省咸阳市武功县高三上学期第二次模拟考试数学(理科)试题(已下线)专题07 三角函数图象及其性质-2020年高考数学(文)母题题源解密(全国Ⅰ专版)(已下线)专题07 三角函数图象及其性质——2020年高考数学(理)母题题源解密(全国Ⅰ专版)(已下线)专题5.9三角函数章末测试(培优卷)-2020-2021学年高一数学尖子生同步培优题典(人教A版2019必修第一册)甘肃省静宁县第一中学2020-2021学年高三上学期第三次模拟考试数学(理)试题河北省衡水市武强中学2020-2021学年高一下学期第一次月考数学试题河南省濮阳市2021-2022学年高一上学期期末数学试题重庆市南开中学校2021-2022学年高一下学期第一次月考数学试题浙江省北斗联盟2022-2023学年高二下学期期中联考数学试题
名校
4 . 已知
,且
,则
的取值范围是____ ,
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cc2bfe433356329b4ac2dfe2b20346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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5 . 在数学史上,为了三角计算的简便并且更加追求计算的精确性,曾经出现过下列两种三角函数:定义
为角
的正矢,记作
为角 的余矢,记作
,则下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b7b2ba487fb7e7063a4f95ea81c94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0255a37af71d190c7ea2eb1f47473a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85366753d63a103ebc4b82cc84118a39.png)
A.函数![]() ![]() |
B.若![]() ![]() |
C.函数![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
2021-01-02更新
|
303次组卷
|
3卷引用:黑龙江省大庆铁人、鸡西一中、鹤岗一中三校2020-2021学年高三上学期联考数学(理)试题
黑龙江省大庆铁人、鸡西一中、鹤岗一中三校2020-2021学年高三上学期联考数学(理)试题江苏省南通市如东县2020-2021学年高一下学期期中数学试题(已下线)压轴题三角函数新定义题(九省联考第19题模式)练
名校
解题方法
6 . 若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbf0e4742a5c972ee9e79bc13e39b1b.png)
,则关于
的命题,以下正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbf0e4742a5c972ee9e79bc13e39b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f230ef8f16dbda82952f9012c82295e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
A.周期为![]() |
B.对称轴方程为![]() |
C.值域为![]() |
D.在区间![]() |
您最近一年使用:0次
2020-11-13更新
|
494次组卷
|
2卷引用:广东省中山纪念中学2021届高三上学期10月月考数学试题
7 . 定义:角
与
都是任意角,若满足
,则称
与
“广义互余”.已知
,下列角
中,可能与角
“广义互余”的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a398610723f9409bc3c939a6ebd3fde0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd51e1f94a4044c16dbdcca6aaf24968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
E.![]() |
您最近一年使用:0次
名校
解题方法
8 . 如图所示,设
,
是平面内相交成
角的两条数轴,
,
分别是与
,
轴正方向同向的单位向量,则称平面坐标系
为
反射坐标系中,若
,则把有序数对
叫做向量
的反射坐标,记为
.在
的反射坐标系中,
,
.则下列结论中,正确的是( )
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759093800960/2572202148265984/STEM/d6669556-9413-4368-abad-ae484efc8758.png?resizew=440)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14069d21d32c724f0ebe3e311f114c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28bba10ce60af27c5817b1faac37a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48bd8a052e56b53a66497b4b55a968a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc155e36276a2226c40a1f4ef7a0f41a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec14a8f7456e74d6c8994bac2ab73de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9c5c7cffee04e1a5545ea43e6f0f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1129c691c26af951624cdc8f77ee9185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52f957ee8898a6915552d1e62ba06cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0817e4c901a4729662505086e7ec6c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7605402b78577eb6fa5b59767e158fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f0f46b3dd282d1e309fb7202050820.png)
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759093800960/2572202148265984/STEM/d6669556-9413-4368-abad-ae484efc8758.png?resizew=440)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
2020-10-16更新
|
1168次组卷
|
4卷引用:重庆市第八中学2021届高三上学期适应性月考数学试题
重庆市第八中学2021届高三上学期适应性月考数学试题(已下线)专题07 平面向量——2020年高考数学母题题源解密(山东、海南专版)(已下线)专题04 平面向量的数量积(客观题)-2021年高考数学二轮复习热点题型精选精练(新高考地区专用)重庆市南开中学2022届高三上学期10月月考数学试题
名校
解题方法
9 . 已知向量
与向量
的对应关系用
表示.
(1)证明:对任意向量
、
及常数
、
,恒有
;
(2)设
,
,求向量
及
的坐标;
(3)求使
(
、
为常数)的向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91b0e5ad368c6da34f2263de056fee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794953fe619ca196431d6beaa0076e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa48cf7be8957cd677297267735bee62.png)
(1)证明:对任意向量
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2c07ad0724802023f1e232aed55ff1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479779070b95c1c2845f0a24dc8d5f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4568d49578f17e744a5d6f6b5d2ed4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17f98350f6070505458786e9953eb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5917359f912d80b0a4ba3269aa91e6dd.png)
(3)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac6d4148ee2d5baa49302c6049eded0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
您最近一年使用:0次
名校
10 . emoji(中文名:绘文字,别称:“小黄脸”)最早源于日本,是指在无线通信中所使用的视觉情感符号,可用来代表多种表情.如今emoji表情已经风靡全球,大有“无emoji,不聊天”的趋势.题图1的“微笑脸”是交流沟通中最常使用的表情符号之一.我们可以用一些适当的函数图象或者是方程的曲线来绘制其近似图象,如题图2.其中,可用曲线
勾勒脸庞,用曲线
,
近似两只眼睛.下列四个函数中,可用其图象来近似描绘嘴巴形状的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/c9b9215e-8b4e-4da8-8e00-6ea39d731a82.png?resizew=203)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25486dc3e404aab8bb0624c5a8cc39f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e96aedcaf728814bca4edf866c87228.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/c9b9215e-8b4e-4da8-8e00-6ea39d731a82.png?resizew=203)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-09-25更新
|
336次组卷
|
2卷引用:广东省深圳市2020-2021学年高二上学期调研数学试题