分别作函数y=2sin(2x-π/6)和y=2sin(2x+π/6)的图像,指出两图像之间的联...

分别作函数y=2sin(2x-π/6)和y=2sin(2x+π/6)的图像,指出两图像之间的联系 函数g(x),f(x)的图像为同频函数图像，g(x)初相为π/6，f(x)初相为-π/6，g(x)图像超前f(x)图像π/6或者说f(x)图像滞后g(x)图像π/6 也即将f(x)图像左移π/6个单位，得到g(x)图像，或将g(x)...

(2)解析：将函数f(x)的图像向左平移π/6个单位得到函数g（x）的图像 G(x)= 2sin(2(x+π/6)-π/6)=2sin(2x+π/6)单调增区间：2kπ-π/2<=2x+π/6<=2kπ+π/2==>kπ-π/3<=x<=kπ+π/6 G(0)=2sin(π/6)=1 G(π/2)=2sin(π+π/6)=-1 ∴g（x）在区间[0...

y=2sin(2x+π/6)+2sin(2x-π/3)=2sin(2x-π/3+π/2)+2sin(2x-π/3)=2cos(2x-π/3)+2sin(2x-π/3)=2√2[sin(2x-π/3)cos(π/4)+cos(2x-π/3)sin(π/4)]=2√2sin(2x-π/3+π/4)=√6 所以sin(2x-π/12)=√3/2=sin(π/3)∵x∈(0,π)∴2x-π/12∈(...

=2sin[2(x-π/6)+2π/3]=2sin(2x+π/3)把h(x)图像上各点的横坐标伸长到原来的4倍，纵坐标不变，得到：g(x)=h(x/4)=2sin(2x/4+π/3)=2sin(x/2+π/3)令x/2+π/3∈[π/2+2kπ，3π/2+2kπ] （k∈Z）x/2∈[π/6+2kπ，7π/6+2kπ] （k∈Z）x∈[π/...

解:2kπbai-π/2≤du2x-π/6≤2kπ+π/2 2kπzhi-π/3≤2x≤2kπ+2π/3 kπ-π/6≤x≤kπ+π/3 (k为整数)单调dao递增区间[kπ-π/6，kπ+π/3]周期=2π/2=π 2x-π/6=kπ+π/2，2x= kπ+2π/3,x= kπ/2+π/3 为 对称轴 方程 ...

横坐标变成原来的1/2,纵坐标不变 →y=sin2x右移π/12 →y=sin2(x-π/12)=sin(2x-π/6)横坐标不变,纵坐标变成原来的2倍 →y=2sin(2x-π/6)下移1个单位 →y=2sin(2x-π/6)-1

解答：y=sin(2x+π/3)=sin2(x+π/6)即将sin2x中的x换成了x+π/6 利用左加右减原则 y=sin(2x+π/3)可由y=sin2x的图像向左平移π/6个单位

1.当2x-π/6=π/2+2kπ,即当x=π/3+kπ,(k∈Z)时,ymax=2×1=2,当2x-π/6=3π/2+2kπ,即x=5π/6+kπ,(k∈Z)时,ymin=2×(-1)=-2,∴值域[-2,2].2.由-π/2+2kπ≤2x-π/6≤π/2+2kπ,得-π/6+kπ≤x≤π/3+kπ,k∈Z,单增区间是[-π/6+kπ,π/3...

平移是针对自变量x而言的,那么原函数y=2sin2x,可以做如此变换y=2sin(2(x+pi/12))就得到你想要的函数了.所以说,应该沿x轴左移pi/12个单位.这题重要的是理解,沿x轴平移多少单位是针对x说的,而不是2x.欢迎追问~

(1)单调递增区间[-π/6+kπ,π/3+kπ),单调递减区间[π/3+kπ,5π/6+kπ);(2)对称轴x=π/3+kπ/2,对称中心(-π/6+kπ/2,0);(3)左移的话，移动π/12+kπ/2个单位,右移的话移动5π/12+kπ/2个单位.以上k为整数 ...