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将函数F(x)=sin(2x+π6)的图象分别向左、右平移...

将函数f(x)=sin(2x+π6)的图象向左平移φ个单位,得到图象所对应的函数解析式为:y=sin(2x+2φ+π6),由该函数图象关于y轴对称,得2φ+π6=kπ+π2,k∈Z,当k=0时φ取得最小正值π6;将函数f(x)=sin(2x+π

向右平移π/6个单位所以是y=sin[2(x-π/6)+π/6]即y=sin(2x-π/6)

X=0时 f(x)=sin(2x+π/6+φ)=1 π/6+φ=π/2 φ=π/3

f(x)=sin(2x+π/6) =sin[(2x-π/3)+π/2] =cos(2x-π/3) =cos2(x-π/6)y=cos(2x+π/4) =cos2(x+π/8)则π/8-(-π/6)=7π/24即要将函数f(x)=sin(2x+π/6)的图像向左平移7π/24个单位可得到y= cos(2x+π/4)

将函数f(x)=sin(2x+θ)(-π/20)个长度单位后得到g(x)图像,若f(x),g(x)图像都经过(0,√3/2) 求φ 解析:∵函数f(x)=sin(2x+θ)(-π/2向右平移φ个单位g(x)=sin(2x+θ-2φ) ∵f(x),g(x)图像都经过(0,√3/2) ∴sin(θ)=sin(θ-2φ)=√3/2==>θ=π/3,θ-2φ=2π/3==>φ=-π/6 ∵φ>0 ∴φ=-π/6+π=5π/6

f(x)=sin(2x+φ)向左平移π/6后,函数为:f(x)=sin(2(x+π/6)+φ)=sin(2x+φ+π/3) f(x)=sin(2x+φ+π/3),f(-x)=sin(-2x+φ+π/3) 偶函数有:f(x)=f(-x)于是:有:sin(2x+φ+π/3)=sin(-2x+φ+π/3) sin(2x+φ+π/3)-sin(-2x+φ+π/3)=0 和差化积:2sin(2x)cos(φ+π/3)=0 cos(φ+π/3)=0 所以:φ+π/3=kπ+π/2,k∈Z 于是最小值:φ=kπ+π/2 - π/3= π/2 -π/3=π/6

∵函数f(x)=2sin(2x+π/3)的图像向右平移m个单位,∴m>0,函数f(x)=2sin(2x-2m+π/3)∵函数f(x)=sinx关于x=π/2对称∵f(x)=2sin2x关于x=π/4对称,∴要使函数f(x)=2sin(2x-2m+π/3)的图像关于x=π/2对称 -2m+π/3=-1/4π+k/2π∵m>0∵最小值为m=7/24π

设f(x)=sin(2x+π 6 ),得图象向右平移π 6 个单位后,得到的表达式为f(x-π 6 )=sin[2(x-π 6 )+π 6 ]=sin(2x-π 6 )对于函数y=sin(2x-π 6 ),令2x-π 6 =π 2 +kπ,得x=1 2 kπ+π 3 ,k∈Z∴变换后的函数图象的对称轴方程为:x=1 2 kπ+π 3 ,k∈Z取k=0,得x=π 3 ,故选:C.

将函数f(x)=sin(1 2 x+π 6 )的图象向左平移φ(0得到y=sin[1 2 (x+φ)+π 6 ]=sin(1 2 x+1 2 φ+π 6 ),再将所得图象上各点的横坐标缩短为原来的倍1 ω (ω>0)倍,纵坐标不变,得到函数y=g(x)=sin(ω 2 x+1 2 φ+π 6 )的图象,∵函数y=g(x)是周期为π的偶函数,∴T=2π ω 2 =4π ω =π,即ω=4,1 2 φ+π 6 =π 2 +kπ,k∈Z,∵0∴φ=2π 3 .故选:B.

将f(x)=2sin(2x- π 6 )的图象向左平移m个单位,得函数g(x)=2sin(2x+2m- π 6 )的图象,则由题意得2* π 6 +2m- π 6 =kπ+ π 2 (k∈Z),∴m= kπ 2 + π 6 (k∈Z),∵m>0,∴当k=0时,mmin= π 6 .故选:B.

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