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1 . 正弦最初的定义(称为古典正弦定义)为:在如图所示的单位圆中,当圆心角
的范围为
时,其所对的“古典正弦”为
(
为
的中点).根据以上信息,当圆心角
时,
的“古典正弦”除以
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/21/41eaa128-da39-4419-8229-93dcd3900762.png?resizew=124)
A.1 | B.![]() | C.![]() | D.0 |
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2 . 已知函数
的部分图象如图所示,且
,则下列说法正确的为( )
![](https://img.xkw.com/dksih/QBM/2021/3/1/2668506683334656/2672310691610624/STEM/b9e9af6d-6f94-43d0-971b-878f044ad158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd778388b12b9ee6d5d3cc84286bd8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcca7abad3fcea8197201c4aa3bda43.png)
![](https://img.xkw.com/dksih/QBM/2021/3/1/2668506683334656/2672310691610624/STEM/b9e9af6d-6f94-43d0-971b-878f044ad158.png)
A.函数![]() |
B.对任意![]() ![]() |
C.若函数![]() ![]() ![]() ![]() |
D.要得到函数![]() ![]() ![]() |
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3 . 已知函数
(其中
),将其图象上所有的点向左平移
个单位长度得到的新函数图象关于原点对称.
(1)求
所有可能取值组成的集合;
(2)若函数
在
单调递减,求
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dc7d27b2848707a1724ac2f1f110176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b909bbcdcb41be76adc4b5e9544a59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9518d59e737e3ac698165c5ec17ba636.png)
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4 . 已知不等式
的解集为
,若
中只有唯一整数,则称A为“和谐解集”,若关于
的不等式
在区间
上存在“和谐解集”,则实数
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8870876779e79db7033f2617b8535eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-02-06更新
|
1158次组卷
|
5卷引用:河北省衡水中学2023届高三上学期三调数学试题
5 . 已知定义在区间
上的函数
的图象关于直线
对称,当
时,函数
.
(1)求
的表达式;
(2)若关于
的方程
有解,那么将方程在
取某一确定值时所求得的所有解的和记为
,求
的所有可能取值及相应
的的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdf32539859901c510ec15f8664b436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15f4b5d828cf068e7044db72c504428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da3023b0765cfb1b268e29e1d01de0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f71f1db49c0863ea542fedcd3c34d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f71f1db49c0863ea542fedcd3c34d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 设向量
,
,
.
(1)若A、B、C三点共线,求实数x的取值;
(2)若
,
的夹角为锐角,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de281d37c92612e9837a4a69fb725d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5931d766d63c8e09eb6daf7cde5277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3345267e3dad49c7eacdb0abc104f3a4.png)
(1)若A、B、C三点共线,求实数x的取值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
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解题方法
7 . 如图,
分别是等腰梯形
的边
上的动点,
,其中
为定值,
,设
,其中
.
,求出
的表达式;
(2)证明:
的余弦值与
的取值无关;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596d41b6556f383445536d1c534ac182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f07948e9258b482a2164ac871f90f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18fec3e4a4fbc7b3e0e037ce650023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d91513d2e546a5a0b5fd42379db8df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e72cf7374a65ced433b6fa113ef57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e2be3e9225c71609248299caa49432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192c2f1059f6e05d44df048f5fdca04b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db625151987f893816de66b15d9e699.png)
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8 . 已知函数
.
(1)若
,求x的取值;
(2)若对于任意
,都有
成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45883a911a321b63aee4fc9be786061e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9c48e36f2c35dd8308029445332aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fce0b7ef89dc5ea77542985ee152ff.png)
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解题方法
9 . 已知
,
.
(1)若
与
垂直,求实数
的范围;
(2)若
与
夹角为锐角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e745905cf02d7165c2a2dfddcee05f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bfa9f707159864b8b3e2f308493738e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dba87f865b15f682f21aff21108690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b18ff77d83bcc3d89a083e1841a3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dba87f865b15f682f21aff21108690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b18ff77d83bcc3d89a083e1841a3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
10 . 给出以下命题正确命题的选项为( )
A.不等式![]() ![]() ![]() |
B.函数![]() |
C.定义运算![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.函数![]() ![]() ![]() ![]() |
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