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已知w>0,0<φ<π,(π/4,0),(3π/4,0)是函数F(x)=sin(w...

f(x)=sin(wx+π/4)(w>0)的减区间由(2k+1/2)π

已知函数f(x)=Asin(wx+φ)(其中A>0,w>0,0φ=π/4; -π/4+φ=π==>φ=5π/4>π/2 ∴f(x)=Asin(x+π/4) f(π/2)=Asin(π/2+π/4)=1==>3π/4=π-arcsin(1/A) arcsin(1/A)= π/4==>1/A=√2/2==>A=√2; ∴A=√2,w=1,φ=π/4==>f(x)=√2sin(x+π/4) (2)解析:设0√2/2(sinθ+c...

已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|0,w>0,|φ|T=4π==>w=2π/T=1/2 ∴f(x)=2sin(1/2x+φ) ∵f(x)图像关于直线x=π/3对称, ∴f(x)在Y轴右侧第一个对称轴为:wx+φ=π/2==>x=(π-2φ)/(2w) 令(π-2φ)/(2w)=π/3==>(π-2φ)=π/3==>φ=π/3 ∴f(x)=2sin(1/2x+π/3) (2...

cosωx - sinωx = sqrt(2) (cosωx cosπ/4 - sinωx sinπ/4) = sqrt(2) cos(ωx + π/4) 该函数在 2kπ

已知函数f(x)=Asin(x+φ)(a>0,0cosβ=12/13==>sinβ=5/13 f(α-β)=sin(α-β+π/2)=cos(α-β)=cosαcosβ+sinαsinβ =36/65+20/65=56/65

sin增 则2kπ-π/2

结论:B 在[0,2π)内 p(sinα-cosα,tanα)在第一象限的充要条件是 sinα-cosα>0,且tanα>0 π/4

已知函数f(x)=Asin(ωx+φ)(A>0,ω>0,00,0w=2π/T=3/2 ∴f(x)=2sin(3/2x+φ) f(π/6)=2sin(π/4+φ)=2==>π/4+φ=π/2==>φ=π/4 ∴f(x)=2sin(3/2x+π/4) (2)解析:设g(x)=[f(x-π/12)]²=4(sin(3/2x+π/8))^2=2-2cos(3x+π/4) 单调递增区:2kπ

其图像经过点M(π/3,1/2) 代入f(x)=sin(x+φ) 1/2=sin(π/3+φ) ∵0

不能啊 即sinwx最小是-1 此时wx=2kπ-π/2 w>0 -wπ/3

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