已知函数f(x)=2sinxcos
2![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707016_ST/0.png)
+cosxsinθ-sinx(0<θ<π),在x=π处取最小值.
(Ⅰ)求θ的值;
(Ⅱ)在△ABC中,a,b,c分别是角A,B,C的对边,已知a=1,b=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707016_ST/1.png)
,f(A)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707016_ST/2.png)
,求角C.
考点分析:
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下列命题:
(1)若函数f(x)=lg(x+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/0.png)
),为奇函数,则a=1;
(2)函数f(x)=|sinx|的周期T=π;
(3)已知
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/1.png)
,其中θ∈(π,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/2.png)
),则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/3.png)
(4)在△ABC中,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/4.png)
=a,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/5.png)
=b,若a•b<0,则△ABC是钝角三角形
( 5)O是△ABC所在平面上一定点,动点P满足:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707015_ST/6.png)
,λ∈(0,+∞),则直线AP一定通过△ABC的内心.
以上命题为真命题的是
.
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707014_ST/images0.png)
已知函数f(x)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707014_ST/0.png)
,若函数g(x)=f(x)-m有3个零点,则实数m的取值范围是
.
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过点A(1,2)且与原点距离最大的直线方程是
.
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已知c是椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707011_ST/0.png)
的半焦距,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707011_ST/1.png)
的取值范围是( )
A.(1,+∞)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707011_ST/2.png)
C.(1,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707011_ST/3.png)
)
D.(1,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930270746/SYS201311031024209302707011_ST/4.png)
]
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