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已知函数f(x)=Asin(wx+φ)(A>0,w>0,|φ|<π/2)图像关...

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...

已知函数f(x)=Asin(wx+φ)(A>0,w>0,0w=2π/2π=1 ∴f(x)=Asin(x+π/4)==>f(π/2)=Asin(π/2+π/4)=Acosπ/4=1==>A=√2 ∴f(x)的解析式为f(x)=√2sin(x+π/4) (2)解析:∵f(θ)=√2sin(θ+π/4)=1/3,且0

(1)解析:∵f(x)=Asin(wx+φ)(A>0,w>0,| φ|T=2π==>w=2π/T=1 ∴f(x)=2sin(x+φ)==> f(5π/6)=2sin(5π/6+φ)=2==>5π/6+φ=π/2==>φ=-π/3 ∴f(x)=2sin(x-π/3) (2)解析:设g(x)=f(2x+π/3)+f^2(x+π/3)>0 g(x)=2sin(2x)+4sin^2(x)=2(sin(2x)-cos2x)+2=2√2sin(...

函数fx=Asin(wx+φ)(A>0W>0 |φ|T=π==>w=2 ∴f(x)=sin(2x+φ)==> f(π/6)=sin(π/3+φ)=1 π/3+φ=π/2==>φ=π/6 ∴f(x)=sin(2x+π/6) (2)解析:g(x)=f(x)-cos2x= sin(2x+π/6)-cos2x=sin(2x-π/6) 单调增区间:2kπ-π/2

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fx=Asin(wx+φ)(A>0,W>0,O0,OT^2=16 ==>T=4==>w=2π/4=π/2 A=|AC|sinπ/4=T/4=1 ∴f(x)=Acoswx=cos(π/2x) ∴f(1)=cos(π/2)=0

已知函数f(x)=Asin(ωx+φ)(A>0,ω>0,|φ|ω=2 ∴f(x)=2sin(2x+π/6) (2)解析:g(x)= 2sin(2(x+π/3)+π/6)=2sin(2x+5π/6) 单调递增区间:2kπ-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

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y=Asin(wx+y)A>0 w>0 00 0w=2,A=2 ∴f(x)=2sin(2x+φ) f(π/6)=2sin(π/3+φ)=2==>π/3+φ=π/2==>φ=π/6 ∴f(x)=2sin(2x+π/6)

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