【答案】
分析:(1)直接根據(jù)向量共線對(duì)應(yīng)的結(jié)論得到tanx=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/0.png)
,再結(jié)合齊次式的應(yīng)用即可求出結(jié)論;
(2)先根據(jù)二倍角公式以及輔助角公式對(duì)所求函數(shù)進(jìn)行整理,再結(jié)合余弦函數(shù)的定義域和值域即可求出結(jié)論.
解答:解:(1)∵
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/1.png)
∥
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/2.png)
時(shí),
∴-3cosx=2sinx,
∴tanx=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/3.png)
.
3cos
2x-sin2x=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/5.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/6.png)
.
(2)f(x)=(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/7.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/8.png)
)•
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/9.png)
=cos
2x-sinxcosx+10
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/10.png)
-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/11.png)
sin2x+10=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/12.png)
cos
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/13.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/14.png)
.
∵x∈
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/15.png)
.
∴-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/16.png)
≤2x+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/17.png)
≤
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/18.png)
,
∴-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/19.png)
≤
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/20.png)
cos
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/21.png)
≤
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/22.png)
,
∴10≤
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/23.png)
cos
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/24.png)
+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/25.png)
≤
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/26.png)
,
即f(x)的值域?yàn)?img src="http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131101231952008156623/SYS201311012319520081566025_DA/27.png">.
點(diǎn)評(píng):本題主要考查了平面向量數(shù)量積的應(yīng)用,和兩角和公式,二倍角公式的運(yùn)用.三角函數(shù)的基本公式較多,注意多積累.