某车间为了制作某个零件,需从一块扇形的钢板余料(如图1)中按照图2的方式裁剪一块矩形钢板ABCD,其中顶点B、C在半径ON上,顶点A在半径OM上,顶点D在
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456016_ST/0.png)
上,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456016_ST/1.png)
,ON=OM=1.设∠DON=θ,矩形ABCD的面积为S.
(Ⅰ)用含θ的式子表示DC、OB的长;
(Ⅱ)试将S表示为θ的函数;
(Ⅲ)求S的最大值.
考点分析:
相关试题推荐
已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/0.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/1.png)
=(-2,0).
(Ⅰ) 求向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/2.png)
-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/3.png)
的坐标以及
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/4.png)
-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/5.png)
与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/6.png)
的夹角;
(Ⅱ)当t∈[-1,1]时,求|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/7.png)
-t
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456015_ST/8.png)
|的取值范围.
查看答案
已知函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456014_ST/0.png)
.
(Ⅰ)求f(x)的单调递减区间;
(Ⅱ)设α是锐角,且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456014_ST/1.png)
,求f(α)的值.
查看答案
如图,在正方形ABCD中,M是边BC的中点,N是边CD上一点,且CN=3DN,设∠MAN=α,那么sinα的值等于
.
查看答案
函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456012_ST/0.png)
的最小正周期是
,它的图象可以由y=sin2x的图象向左平移
个单位得到.
查看答案
已知
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456011_ST/0.png)
,设
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222949811945652/SYS201311012229498119456011_ST/1.png)
,那么实数λ的值是
.
查看答案