1 . 已知函数
.
(1)求函数
的最小正周期和对称中心;
(2)求函数
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f69de3ad887fd13dd3202a12db09670.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c40aeeec9aa219c0af917fd34258282.png)
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2 . 已知函数
,则下列关于函数
的结论中,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52482c16db2f6629408c55f9cb3753fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.最大值为1 | B.图象关于直线![]() |
C.既是奇函数又是周期函数 | D.图象关于点![]() |
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3 . 已知函数
,其图象关于点
中心对称.
(1)求函数
在
上的值域;
(2)将
图象上各点的横坐标缩短到原来的
倍,然后再向右平移
个单位长度得到
的图象.若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd80dee83f639ae267b30843b16815f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec245c6a0836cb8138a349b2464000b5.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efd291c11b2a5629b6b4b0ea0dead85.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02492a7dc0aed4f0589ceb2edf783834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c37c65e4ae349306e3b1c877236575c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483d7559ab4408d8f7fa63e14313a818.png)
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解题方法
4 . 五一假期,杭州吴山广场的鸽子吸引了众多游客.热爱摄影的小华计划在广场一角架设一台可转动镜头的相机,希望可以捕捉到鸽子的展翅瞬间.小华设计了一个草图,为简化模型,假设广场形状为正方形,边长为1,已知相机架设于A点处,其可捕捉到图像的角度为
,即
,其中P,Q分别在边
,
上,记
.
与
相交于点R,当
时,
(ⅰ)求线段
的长;
(ⅱ)求线段
的长;
(2)为节省能源,小华计划在广场上人员较多的时段关闭相机镜头的自动转动功能,为使相机能够捕捉到的面积(即四边形
的面积记为S)最大,
应取何值?S的最大值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7ea65be0351e839d45d598dfb254b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d5e2024c868a5b6fd6da53881422e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233833048b34c91d3221ca3aa88468a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff937114137ebad16c7576bf2849b00.png)
(ⅰ)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab64bf465405cd87bb03f8cb61cb315.png)
(ⅱ)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0998f562e478421adae3377aa700e5.png)
(2)为节省能源,小华计划在广场上人员较多的时段关闭相机镜头的自动转动功能,为使相机能够捕捉到的面积(即四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be87b8293fbf86e305d09cc19fd42f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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5 . 对于任意的
恒成立,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae71ca220cf385a9ed695ed78902058d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6 . 已知在锐角
中,三个内角A、B、C的对边分别为a、b、c,
则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36ec31cfd615abfbee3ed2f4a1d8883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49386fb1d7557c1dc9956a4495e2ca9.png)
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7 . 若复数
,满足
(
为虚数单位),则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f543c26ef2de07fb132ba386a8b498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2acba428fab1522910d1e0a3948ac8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 设函数
.
(1)若角
满足
,求
的值;
(2)求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6755307e13345d62df24a38e725390f2.png)
(1)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20818a7a5042d5f832e2bd9af4c6fa66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1a95a3dfd554520c12b9e7ff4de273.png)
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解题方法
9 . 在
中,角
的对边分别为
,若
,
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d786bbb41453cde91a48b7292937e8be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
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解题方法
10 . 在锐角
中,记
的内角
的对边分别为
,
,点
为
的所在平面内一点,且满足
.
(1)若
,求
的值;
(2)在(1)条件下,求
的最小值;
(3)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd93e8d3e3bd15eca0e309f931ae8f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5baac0dd8be4c646a32213e3a979f9d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f6894da6183fb8b8e7ac9b9f98cdb82.png)
(2)在(1)条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a442e21ce6d4de5fd2392ad94f7dace3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8954ac84d5a64358d2876a62f2a439b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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