解题方法
1 . 下列说法正确的是( )
A.若点![]() |
B.角θ的终边与圆心在原点、半径为r的圆的交点为![]() |
C.长度等于半径的![]() ![]() |
D.钟表时针走过2小时,则时针转过的角的弧度数为![]() |
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解题方法
2 . 在平面直角坐标系xOy中,单位圆
与x轴的正半轴及负半轴分别交于点A、B,角
的始边为OA,终边与单位圆交于x轴下方一点P.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/6da3729e-ed70-433b-bbc1-e8d9dfd71434.png?resizew=163)
(1)如图,若
,求点Р的坐标;
(2)若点P的横坐标为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/6da3729e-ed70-433b-bbc1-e8d9dfd71434.png?resizew=163)
(1)如图,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eef58d640049ffde7a70129106e92b.png)
(2)若点P的横坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07dbd8a44d6c8368f67525b669a7ceb.png)
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解题方法
3 . 已知
.
(1)求
;
(2)若角
的顶点为坐标原点,始边与
轴的非负半轴重合,终边上有两点
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fd99a7223aa1d3c000b310d9b81fb3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e5b2ae22ce237cb72d4d01f0cf4f27.png)
(2)若角
![](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/06f0f6be19fc4543d092090ac59d6ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b435aeaf6867f42b6b23d7e989f99f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
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4 . 如图,
于D,
于E,BD与CE相交于
,则图中线段的比不能表示
的式子为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/26/4be69b8c-9234-4791-b9ff-aa371e97e8e4.png?resizew=182)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f913298f0fae9f55377a8deab9f099dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b01adc561735ff5be9bb97266918f2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/26/4be69b8c-9234-4791-b9ff-aa371e97e8e4.png?resizew=182)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 在①已知角
的始边与x轴的非负半轴重合,终边落在直线
上;②
,在这两个条件中任选一个,补充在下面问题中,并对其求解.
问题:已知
满足___________,求值:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f8d270181ba54e2b1f45fa40f33a99.png)
问题:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8d5aea3e965ff9f4dc563cc94399a1.png)
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解题方法
6 . 已知
为坐标原点,点
的初始位置坐标为
,线段
绕点
顺时针转动
后,点
所在位置的坐标为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290092e2e5ec15af1f6f294fdd208603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ff7caec4fdd8fb54a3ffbff9692414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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名校
解题方法
7 . 下列说法正确的是( )
A.角![]() ![]() |
B.圆的一条弦长等于半径,则这条弦所对的圆心角等于![]() |
C.经过![]() ![]() |
D.若角![]() ![]() ![]() ![]() |
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2023-01-11更新
|
1078次组卷
|
5卷引用:湖北省武汉外国语学校2022-2023学年高一上学期期末数学试题
解题方法
8 . 如图所示,角
的终边与单位圆
交于点
,
,
轴,
轴,
在
轴上,
在角
的终边上.由正弦函数、正切函数定义可知,
,
的值分别等于线段
,
的长,且
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/8335edab-ba09-44ec-a074-7c588f7f970e.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec40adf62bc48e014d76647f1eabce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c5a05a11f731194a845e68a0479ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3aa7196edf804545a57340786698677.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/8335edab-ba09-44ec-a074-7c588f7f970e.png?resizew=180)
A.函数![]() |
B.函数![]() ![]() |
C.函数![]() ![]() |
D.函数![]() ![]() |
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解题方法
9 . 1874年欧拉第一次提出将角置于圆内,以有向线段与半径的比值定义三角函数.如图,在单位圆中,定义角
的正弦为有向线段MP,角
的余弦为有向线段OM.若在单位圆内,角
和角
均以Ox轴为始边,两角的终边关于
轴对称,且对应正弦的值均为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c634aa65493615fbb40f1352a88c5aa3.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c634aa65493615fbb40f1352a88c5aa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/26/7600a162-548b-4cd4-9103-c5d793ce5e82.png?resizew=136)
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10 . 知道在直角三角形中,一个锐角的大小与两条边长的比值相互唯一确定,因此边长与角的大小之间可以相互转化.与之类似,可以在等腰三角形中建立边角之间的联系,我们定义:等腰三角形中底边与腰的比叫做顶角的正对
.如图,在
中,
.顶角
的正对记作
,这时
.容易知道一个角的大小与这个角的正对值也是相互唯一确定的.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/5b08a58e-a870-4476-94b0-748fead6aa54.png?resizew=112)
根据上述对角的正对定义,解下列问题:
(1)
的值为( )
A.
B.
C.
D.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)对于
,
的正对值
的取值范围是______.
(3)已知
,其中
为锐角,试求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab3e912f74f80b0878f90c88d42af80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf41b94bb22f385601fa21c3cf435470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea36188262b6bbf9098ba084b1d66bc8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/5b08a58e-a870-4476-94b0-748fead6aa54.png?resizew=112)
根据上述对角的正对定义,解下列问题:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d9d97b81f939119268d8006bedac0a.png)
A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a54e7d6e547a5d4850edc4025eeacc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73738e78a4d8e6df0129113ada99f4fc.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bc052a11cf1a01445992672dde2836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4777985fe308c220d5827aae7b93f4c.png)
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