解题方法
1 . 正方形
的边长为6,
,
分别为线段
,
上的动点.
(1)若
是
的三等分点
,求
的值;
(2)当点
在
边上运动时,始终保持
,当点
运动到什么位置时,线段
最短.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c330983114d20b630093055ac267db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146c183051f41ac154a9ff4d74d3d5cc.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce726bceb02452bb4e5ed6b00fa94e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
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解题方法
2 . 已知斜三角形
.
(1)借助正切和角公式证明:
.
并充分利用你所证结论,在①②中选择一个求值:
①
,
②
;
(2)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(1)借助正切和角公式证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f846e5859aab52461b125a83652ec9.png)
并充分利用你所证结论,在①②中选择一个求值:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7798db106b4bed40fd7b43a9eaeb463.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6508e636cfd77c0a0406b3fbf3b70213.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc19955c1f24f90d36c68aba23bebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30f03a31c8a873bfcf7287e45b6c6a0.png)
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3 . 在平面直角坐标系中,点
为坐标原点,已知
,
,
.
(1)求向量
与
夹角的余弦值;
(2)若点
满足
,
,求点
的坐标及向量
在向量
上的投影向量的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b2cc0d2f6d3eee9a33db83e0c0830d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8159754fa962579d7dcb79da0ba1908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02eea25799267c0a948a6a9ffab2ffd9.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8978ecc859804a7c23c2cc8c9175677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1206fd4b58cd793401ef61fd2ff22ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f28b09c6074898b0bf992928336eb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
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4 .
的一般结构是
.站在三角换元的角度,就是利用同角三角函数中的平方关系,对代数式中的两数和或平方和为常数的结构进行三角代换以挖掘代数式中的隐含条件来解决问题.研究函数
,求出
的值域是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2302bd8fbae724ad0aa0dd1a2c318968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8cc033b39e6328fa6c478bdb5c7a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cbb353e903b72f2e59f025a8e3179f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5 . 某同学在利用正弦定理和余弦定理解三角形的研究性学习中发现,用边角互化的思想求出以下三个式子的值都等于同一个常数.
(1)
;
(2)
;
(3)
;
这个常数为________ ,将该同学发现的结论一般化后表述出来为________ .
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7cc3f9cdac66bfcbb4e25547a78a5a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5741640c81fc54484403a3b1495a2f11.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf279f5d03cf5d1abe3541fc17b77fd.png)
这个常数为
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解题方法
6 . 在
中,
,
,
,则
的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48ba2b1a54ce81c8ce16a5357302cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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7 . 对于函数
,若存在大于零的常数
和非零常数
,使得当
取定义域中的每一个值时,都有
,那么
称为“类周期函数”,
叫做“类周期”.下列四个命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3281ac9e36c20d31cf4bc12548b46f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
A.函数![]() ![]() |
B.函数![]() |
C.函数![]() |
D.设函数![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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8 . 已知函数
的一部分图象如图所示.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6309e18f51f43800c0a16205c6a491b.png)
A.函数![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.当![]() ![]() |
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9 . 已知平面向量
,
在由正方形组成的网格中的位置如图所示(网格中面积最小的正方形边长为1),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 在
中,角
,
,
的对边分别为
,
,
,其中
,
,若
,
,则
的最小值为( )
![](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/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e842fe98ec9ded46916a7443969495e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9ec09e1ad28e85ea0c2345127c8fff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6732580ffff616408c0985d7175a4c2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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