函数f(X)=sin(wx+φ)(w>0,|φ|

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 07:33:33

函数f(X)=sin(wx+φ)(w>0,|φ|
函数f(X)=sin(wx+φ)(w>0,|φ|<π/2)在它的某一个周期内的单调减区间是 [5π/12,11π/12]
将y=f(x)的图象先向右平移π/6个单位,再将图像上所有点的横坐标变为原来的1/2倍（纵坐标不变）,所得到的图象对应的函数记为g(x),求函数g(x)在[π/8,3π/8]上的最大值和最小值

函数f(X)=sin(wx+φ)(w>0,|φ|
依题意：T/2=11π/12-π/12=π/2
∴T=π,由2π/w=π得：w=2
∴f(x)=sin(2x+φ)
∵ [5π/12,11π/12]是单调减区间
∴f(5π/12)=sin(2*5π/12+φ)=1
∴5π/6+φ=2kπ+π/2,k∈Z
∵,|φ|

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