题目内容
已知向量![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008068452550.jpg)
函数
且最小正周期为
.
(I)求函数
的最大值,并写出相应的X的取值集合;
(II)在
中,角A,B, C所对的边分别为a, b,c,且
,c=3,
,求b的值.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008068452550.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806861635.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008068761048.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806892443.jpg)
(I)求函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806907574.jpg)
(II)在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806923661.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806939742.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806954903.jpg)
(Ⅰ)∵m=
,n=
,
∴∣m∣=
,
m·n=![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008070321045.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807048816.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008070631079.png)
,
∴
.…………………………
………………………4分
由
,解得ω=1.
∴
.
∴此时
(k∈Z)
,即
(k∈Z),
即当x∈{x|
,k∈Z}时,f (x)有最大值3.………………………7分
(Ⅱ)∵ f (B)=2,
∴ 由(
1)知
,即
.
于是
,解得
.………………………………………10分
由
,即
,解得a=8,
由余弦定理得 b2=a2+c2-2accosB
=49,
∴ b=7.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200806970707.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807001929.png)
∴∣m∣=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807017837.png)
m·n=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008070321045.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807048816.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008070631079.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807079869.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008070951067.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807110164.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807126646.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008071411003.png)
∴此时
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807173793.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807173156.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807188641.png)
即当x∈{x|
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807188641.png)
(Ⅱ)∵ f (B)=2,
∴ 由(
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807329156.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807344898.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807360863.png)
于是
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807375708.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807391505.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232008074071098.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807422810.png)
由余弦定理得 b2=a2+c2-2accosB
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823200807438788.png)
∴ b=7.
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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