已知
,
.
(1)求
的值;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a9d1b8269a6ff06ee8a1f45cfe72a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06f37bd322af6e273ceb66bac49a716.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf73d07b3b9c0f5055256998a5d68527.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d396bfbd587606d9ef885f28b62552dc.png)
更新时间:2023-02-17 16:21:12
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【推荐1】已知
(
且
),求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92110ee8664c15f3b9429cfc2e1b3028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3d43f3e7109d1e4173ee4993c9a148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
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【推荐2】在
中,内角A,B,C的对边分别为a,b,c,且
.
(1)求
;
(2)
的内切圆半径为
,
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b230c6db4c2235e6256342c709b6c967.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32e2f2d7147cf1699fbfdef9cf4af74.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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【推荐1】(1)解不等式:
;
(2)已知
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e591984806a18b6d51a9fb87653f621.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75548e867f471abe608b8f0e40b71a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d779d0b4fb199de2a652a687d387fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ff709f47b4773d1d3982980695d074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b04da7eac640b5b735da7fb5da8cfd.png)
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【推荐2】已知
是第二象限角,且____________ . 从下面三个条件中选一个解答;
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993cbe09df35301c39974837affe01de.png)
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947dee04d437ec13690b386dedd28d01.png)
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365eb711803233e1416a60a10e92d5df.png)
(1)求
和
.
(2)
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993cbe09df35301c39974837affe01de.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947dee04d437ec13690b386dedd28d01.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365eb711803233e1416a60a10e92d5df.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6369cd1db768436809404b1f3c4132c0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06a3415437f0da47c3f64e18cc4b127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
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【推荐1】已知
中,角A,B,C的对边分别是a,b,c,且
.
(1)求角A的大小:
(2)若
,
,D为
中点,点E在
上且满足
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b0c350d4bb3ebd2c6733ecc56741f6.png)
(1)求角A的大小:
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
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【推荐2】在
中,角
所对的边分别为
.已知
,
,
.
(1)求
的值;
(2)求
的值;
(3)求
的值.
![](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/f7fa79a550591eb9e1bd07bced3a08fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5978b3692daed80e12a18b5a68ed2d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3706d23fd33958c6cb8e2e78aac2cfe.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32e2f2d7147cf1699fbfdef9cf4af74.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e64c143dc5ec927ce39e129760f7bf2.png)
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【推荐3】结合下面的阅读材料,研究下面两个问题.
(1)一个三角形能否具有以下两个性质(i)三边是连续的三个偶数,(i)最大角是最小角的2倍;
(2)一个三角形能否具有以下两个性质(i)三边是连续的三个奇数,(i)最大角是最小角的2倍.
阅读材料:习题(人教版必修5第一章复习参考题B组3)研究一下,一个三角形能否具有以下性质:
(1)三边是连续的三个自然数;(2)最大角是最小角的2倍.
解:(方法一)设三角形三边长分别是
,
,
,三个角分别是
,
,
,
由正弦定理,
,所以
:
由余弦定理,
,
所以
,
化简得
,
所以![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
三角形的三边分别是
,可以验证此三角形的最大角是最小角的
倍.
(方法二)先考虑三角形所具有的第一个性质:三边是连续的三个自然数,
(1)三边长不可能是
这是因为
,与三角形任何两边之和大于第三边;
(1)一个三角形能否具有以下两个性质(i)三边是连续的三个偶数,(i)最大角是最小角的2倍;
(2)一个三角形能否具有以下两个性质(i)三边是连续的三个奇数,(i)最大角是最小角的2倍.
阅读材料:习题(人教版必修5第一章复习参考题B组3)研究一下,一个三角形能否具有以下性质:
(1)三边是连续的三个自然数;(2)最大角是最小角的2倍.
解:(方法一)设三角形三边长分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82609af153365dcdc4ab64825a142b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dd0c52aca1675c17b9a019aa7901e3.png)
由正弦定理,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1572cc4e88c14f0c537360a368b7f423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a1597f3620ec4630526e663673aed2.png)
由余弦定理,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6fef75950bf476a5f93737533b2e32.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3b4d15402a44f99d247abe944d06ff.png)
化简得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb623784578945deb88ec4a6acbca3e.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
三角形的三边分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f734712e39d68a541159bf61d865ba69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(方法二)先考虑三角形所具有的第一个性质:三边是连续的三个自然数,
(1)三边长不可能是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73d43981283ac63dbc0d1cfc7426d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc114012e9d5888ca8ac6b6eacd306e.png)
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【推荐1】在平面直角坐标系中,已知角
的顶点为原点,始边为
轴的非负半轴,终边经过点
.
(1)求
的值;
(2)求
旳值.
![](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/6e48ea72fd40ebc8004ff0dfd22ba6c3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f70794fcca63274e3ba369d518feee0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5653b4620620d07b555e4a6c9ff91f6.png)
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【推荐2】在
中,角A,B,C所对的边分别为a,b,c,且满足
.
(1)求角C的最小值;
(2)当C=
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b0914cd974dfefadf7093cc7fc717.png)
(1)求角C的最小值;
(2)当C=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7a55368936281934788044d18ff0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6209806f3aa028c3fd93eaa08b5a106f.png)
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