1 . 已知函数
.
(1)求函数
的最小正周期;
(2)求函数
在区间
上的最小值和最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6891cfb44d44f17bb79b82e85ab79fb8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7466d2055b1e49baea19e7e13cf97b77.png)
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解题方法
2 . 下列化简结果正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知函数
.
(1)求
的最小正周期及单调递增区间;
(2)若
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc84fc7a501d15dc107950120af91b7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3adbb701b7084868e1eabc8780c939b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 已知
,
,
,从下面①,②中选择一个作为已知条件,解答问题:
(1)求
的值;
(2)将
的图象向右平移
个单位得到
的图象,求函数
的单调增区间.
①
的最大值为
;②
.
注:如果选择①和②分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d520c3492f345f7b340f02cfe61d9393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c7859e596710e8525fbc2863afa68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bb6c1ae5d9843039251741d7a252ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0c7f1e377f9d1aa6d1f914b55bfd62.png)
注:如果选择①和②分别解答,则按第一个解答计分.
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5 . 已知
中,角
的对边分别是
,
,
,且
.
(1)求角A的大小;
(2)求
的最大值;
(3)若
,
为
边上靠近B点的三等分点,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516983449108347c9bbf5dd2a72ab3dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90d7f054e8f0346479e1999622f11cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8c463f847a2360d2ce5d2de4f17be4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452e15519f305e5afbc184116b4691a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2758285d3c1d8c16784edbc5f572fc26.png)
(1)求角A的大小;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dfa04ed69eb5e36931c076e0cf3f01e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.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/15c0dbe3c080c4c4636c64803e5c1f76.png)
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6 . 古代数学家刘徽编撰的《重差》是中国最早的一部测量学著作,也为地图学提供了数学基础.现根据刘徽的《重差》测量一个球体建筑物的高度,如图,已知点
是球体建筑物与水平地面的接触点(切点),地面上
,
两点与点
在一条直线上,且在点
的同侧,若在
,
处分别测得球体建筑物的最大仰角为
和
,且
,则该球体建筑物的最高点距离地面为( )
![](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/5963abe8f421bd99a2aaa94831a951e9.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/a2d9a1a93e47dc1e50ba2779ef480724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0ed18bdcdc50e3b52b9366db524d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e4251fb95153f41cb2c70f68b0f9db.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 函数
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d5e99c04d285c057e44af0b739d0b7.png)
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8 . 已知函数
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6abed9e9278a90b492a0ab03858584d7.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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解题方法
9 . 已知函数
.
(1)若函数
,且当
时,
有零点,求实数
的取值范围;
(2)若
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c5135167887fd1092057f7d7c2c9d5.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd1017814e9883c21b17e43703a7272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1e3f55d710b23038928e1cde6e0548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6bba4fae5317676a006246590539f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ff0e5c78c04beea4e773185195da30.png)
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10 . 在
中,内角A,B,C的对边分别为a,b,c,且
.
(1)求角B;
(2)若
为锐角三角形,
,D是线段AC的中点,求BD的长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7cd8020fdf7ae5a64bc25d89293782.png)
(1)求角B;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
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