名校
1 . 由倍角公式
,可知
可以表示为
的二次多项式.对于
,我们有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2104a78b37da636d13e09e5bdb2be10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b752c5b70e8bef980994bfbb88df7cbc.png)
,可见
也可以表示成
的三次多项式.以上推理过程体现了数学中的逻辑推理和数学运算等核心素养,同时也蕴含了转化和化归思想.
(1)试用以上素养和思想方法将
表示成
的三次多项式;
(2)化简
,并利用此结果求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91d0d02d04a3f1b777b0d86e2372e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e039219978242ec380e66de6cf9bab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2104a78b37da636d13e09e5bdb2be10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b752c5b70e8bef980994bfbb88df7cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706585b7d68cd2b99f2f671328c318a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e039219978242ec380e66de6cf9bab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(1)试用以上素养和思想方法将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff1dd2db6f898d70a9adef9a0f2ffad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06680427974d0fb0ca07d306f92d505a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1064e3198a310f74672b7211ba74071.png)
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名校
2 . 已知
.
(1)求函数
的最小正周期;
(2)已知
均为锐角,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1170c8ae33045bea4da61519b91708f7.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c9847b76e02ecdc83577e4ef88902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affef976aac53a7783108bd132cef3c0.png)
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2023-06-21更新
|
1344次组卷
|
7卷引用:陕西省榆林市府谷中学等四校2022-2023学年高二下学期第一次联考理科数学试题
3 . 已知
,
,且
,
.
(1)求
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352dfe6907c582daa7f426d9df59a92a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bc052a11cf1a01445992672dde2836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e86ef3d12d6c2f2125d98cd164f34e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da906f083d3269c880621c1f9839548b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eacde1c42151734fdc60f3001b590de.png)
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解题方法
4 . 在高速公路建设中经常遇到开通穿山隧道的工程,如图所示,A,B,C为某山脚两侧共线的三点,在山顶P处测得三点的俯角分别为
,
,
,现需要沿直线AC开通穿山隧道DE,已知
,
,
,则隧道DE的长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/c4668d2a-1a72-4ad1-8799-6fab2c2a300b.png?resizew=237)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d5a9690d02c2b1e6bbd6fd05225c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68abcbf1e98c4a3f7119d922ec629da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a4cd8610ebbc22728db7f30ceb5543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fae5a3ab64625f75180c8cbbd39a87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea04531fcd729669854a67b62492bdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/c4668d2a-1a72-4ad1-8799-6fab2c2a300b.png?resizew=237)
A.![]() | B.![]() | C.10 | D.![]() |
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2022-07-18更新
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530次组卷
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5卷引用:陕西省咸阳市武功县2022-2023学年高二上学期期中理科数学试题
陕西省咸阳市武功县2022-2023学年高二上学期期中理科数学试题陕西省咸阳市礼泉县2022-2023学年高二上学期期中理科数学试题山东省聊城市2021-2022学年高一下学期期末数学试题(已下线)11.3 余弦定理、正弦定理的应用-【题型分类归纳】2022-2023学年高一数学同步讲与练(苏教版2019必修第二册)(已下线)模块三 专题3 小题满分挑战练(3)(人教B)
解题方法
5 . 计算求值:
(1)计算
的值;
(2)已知
、
均为锐角,
,
,求
的值.
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a497cfa130c80a1c93a49f80ea7aaa83.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b9189638705753a50b5dc1c6ef54ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c740e41a3ad0345cc45155d1c2eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fe57d4fbae536de2e641d9d349fcf1.png)
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名校
6 . 已知
,
(1)求
;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bfb7976230b3b24c2c88f238eac9bf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f71b1446d36d87c4e3f99d5bdb66170.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8d15d62082fdade0a60b18ec26880c.png)
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2022-03-24更新
|
406次组卷
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2卷引用:陕西省西安中学2021-2022学年高一下学期期中数学试题
名校
解题方法
7 . 已知角
的顶点与原点重合,始边与
轴的非负半轴重合,它的终边过点
.
(1)求
的值.
(2)若
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889a5e04c5187fb20415a59ce6adeed5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3954ee7211b046540f98f7b37343f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba80eb5253bed4d4834ebbf39980424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a08a612bc01f3937fab85284d08eab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fe57d4fbae536de2e641d9d349fcf1.png)
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2022-04-26更新
|
327次组卷
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2卷引用:陕西师范大学附属中学2020-2021学年高一下学期期中数学试题
解题方法
8 . 如图,在
中,
是
内部一点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457ca98094e6d6082712d6f37930c340.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/ad092226-95ec-4836-ab84-bd63b56d9dee.png?resizew=126)
(1)求
的长;
(2)求证:
为等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287bc880f8946d297284048d55c60b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457ca98094e6d6082712d6f37930c340.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/ad092226-95ec-4836-ab84-bd63b56d9dee.png?resizew=126)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
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2021-11-01更新
|
208次组卷
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2卷引用:陕西省榆林市定边县第四中学2024届高三上学期高考滚动检测(三)(期中)文科数学试题
名校
解题方法
9 . 在
中,角
所对的边分别为
,
.
(1)求角C的大小;
(2)若
,
的面积
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0ae8e92dd3119d41f2c830ea526516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ace74bfb716753490ebe0e740ff5baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fedc32491b66c5e6f7c11d3931ab8a.png)
(1)求角C的大小;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78a6b3dca848658846591934773c680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2021-07-21更新
|
388次组卷
|
7卷引用:陕西省咸阳市高新一中2022-2023学年高二上学期期中理科数学试题(A卷)
名校
解题方法
10 . 已知
中,角A,B,C的对边分别为a,b,c,
.
(1)若
,求
的值;
(2)若
的平分线交AB于点D,且
,求
的最小值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e459e24a3c880c0aaa155e56a8dde9c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b104867a12d24a353d94858c2fa17c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a24a8f5e8fb89381f8add6549170345.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
2020-05-28更新
|
201次组卷
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2卷引用:陕西师范大学附属中学2022-2023学年高三上学期期中理科数学试题