已知向量
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,b(sinωx,0),且ω>0,设函数f(x)=(a+b)•b+k.
(1)若f(x)的图象中相邻两条对称轴间的距离不小于
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,求ω的取值范围.
(2)若f(x)的最小正周期为π,且当
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时,f(x)的最大值是2,求就k的值.
考点分析:
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已知函数f(x)=Asin(ωx+φ),x∈R(其中A>0,ω>0,0<φ<
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)的周期为π,且图象上一个最低点为
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.
(Ⅰ)求f(x)的解析式;
(Ⅱ)当
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,求f(x)的最值.
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设函数f(x)=(sinωx+cosωx)
2+2cos
2ωx(ω>0)的最小正周期为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439017_ST/0.png)
.
(Ⅰ)求ω的值;
(Ⅱ)若函数y=g(x)的图象是由y=f(x)的图象向右平移
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439017_ST/1.png)
个单位长度得到,求y=g(x)的单调增区间.
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已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439016_ST/0.png)
=(sinθ,cosθ-2sinθ),
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=(1,2).
(1)若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439016_ST/2.png)
,求tanθ的值;
(2)若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439016_ST/3.png)
,求θ的值.
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如图所示,已知O为平行四边形ABCD内一点,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439015_ST/0.png)
=
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,
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=
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,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439015_ST/4.png)
=
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,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101230856715343989/SYS201311012308567153439015_ST/6.png)
=______
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已知定义域为R的函数f(x)=
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是奇函数.
(Ⅰ)求b的值;
(Ⅱ)判断函数f(x)的单调性;
(Ⅲ)若对任意的t∈R,不等式f(t
2-2t)+f(2t
2-k)<0恒成立,求k的取值范围.
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