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已知函数F(x)=Asin(x+φ)(A>0,0<φ<π)x∈R的最大值是1...

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

解由函数f(x)=Asin(ωx+φ)(a>0,ω>0,0

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

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...

解答: (1) 容易求得f(x)=sin(x+π/3) 在g(x)上任意一点(x,y),关于直线对称的点是(π/2-x,y) ∴ sin(π/2-x+π/3)=y ∴y=cos(x-π/3) 即 g(x)=cos(x-π/3) (2) -π/2

(1)解析:由图示:A=2, ∴f(x)=2sin(wx+φ)==>f(0)=2sin(φ)=1==>φ=π/6或φ=5π/6 ∵|φ|x=kπ/w-π/(6w) 由图示下一周期起点为x=11π/12 当k=2时,x=2π/w-π/(6w)=11π/12==>12(12π-π)=6*11πw ∴w=12/6=2 ∴f(x)=2sin(2x+π/6) (2)解析:设0

f(x)=a·tan(ωx+φ)? 相邻零点距离5π/6-π/6=2π/3为最小正周期 ω=π/(2π/3)=3/2 ω·π/6+φ=0 φ=-π/4 ∴f(x)=a·tan(3x/2-π/4) f(0)=a·tan(3x/2-π/4)=-a=-3 ∴a=3 f(x)解析式:f(x)=3tan(3x/2-π/4) (2)3tan(3x/2-π/4)≥√3 tan(3x/2-π/4)≥√3/3=tan(kπ+π/6) ∴k...

1、 T=2π/w=π w=2 最小=-2 所以A=|-2|=2 f(x)=2sin(2x+φ) 过M -2=2sin(4π/3+φ) 4π/3+φ=3π/2 φ=π/6 f(x)=2sin(2x+π/6) 2、 0

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

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