题目内容
(本题满分10分)已知向量
=(cos
,sin
),
=(cos
,sin
),|
|=
.
(Ⅰ)求cos(
-
)的值;
(Ⅱ)若0<
<
,-
<
<0,且sin
=-
,求sin
的值.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704546295.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704577285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704577285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704608316.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704624339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704624339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704702411.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704733485.png)
(Ⅰ)求cos(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704577285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704624339.png)
(Ⅱ)若0<
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704577285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704827420.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704827420.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704624339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704624339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705014402.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195704577285.png)
解:(Ⅰ)(5分)
,
. ---------------------------------------1分
,
.---------------------------------2分
即
. ---------------------------------------------------1分
. ------------------------------------------------------------------1分
(Ⅱ)(5分)∵
, ∴
---------------------1分
∵
,∴
----------------------------------1分
∵
,∴
-----------------------------------------------------1分
∴![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231957056852036.png)
.------------------2分
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231957051231180.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231957051541107.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705326791.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231957053571543.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705373959.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705513866.png)
(Ⅱ)(5分)∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705529934.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705544645.png)
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705575869.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705622832.png)
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705638693.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823195705669731.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231957056852036.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231957057161220.png)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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