已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值
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![已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值](/uploads/image/z/12534638-14-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0fx%3Dsin%28wx%2By%29%28w%3E0%2C0%E2%89%A4y%E2%89%A4%CF%80%29%2C%7Cf%280%29%7C%3D1%2Cfx%E7%9A%84%E5%9B%BE%E5%83%8F%E5%85%B3%E4%BA%8E%E7%82%B9M%283%CF%80%7C4%2C0%29%E5%AF%B9%E7%A7%B0%2C%E4%B8%94%E5%9C%A8%E5%8C%BA%E9%97%B4%E3%80%900%2C%CF%80%7C2%E3%80%91%E4%B8%8A%E5%B8%82%E5%8D%95%E8%B0%83%E5%87%BD%E6%95%B0%2C%E6%B1%82w%2Cy%E7%9A%84%E5%80%BC)
已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值
已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值
已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值
|f(x)|=1 => |siny|=1, 因为0
w*PI/2+PI/2 w0,知w=2/3, 2.
已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值
解析:因为,函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1
当f(0)=1时,f(0)=sin(y)=1==>y=π/4或y=3π/4
所以,fx=sin(wx+π/4)或fx=sin(wx...
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已知函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1,fx的图像关于点M(3π|4,0)对称,且在区间【0,π|2】上市单调函数,求w,y的值
解析:因为,函数fx=sin(wx+y)(w>0,0≤y≤π),|f(0)|=1
当f(0)=1时,f(0)=sin(y)=1==>y=π/4或y=3π/4
所以,fx=sin(wx+π/4)或fx=sin(wx+3π/4)
因为,fx的图像关于点M(3π|4,0)对称
f(3π/4)=sin(w3π/4+π/4)=0==>3w=-1==>w=-1/3
f(3π/4)=sin(w3π/4+3π/4)=0==>w=-1
∴f(x)=sin(-1/3x+π/4)= sin(1/3x+3π/4)
或f(x)=sin(-x+3π/4)= sin(x+π/4)
当f(0)=-1时,f(0)=sin(y)=-1==>y=-π/4或y=-3π/4
所以,fx=sin(wx-π/4)或fx=sin(wx-3π/4)
因为,fx的图像关于点M(3π|4,0)对称
f(3π/4)=sin(w3π/4-π/4)=0==>3w=1==>w=1/3
f(3π/4)=sin(w3π/4-3π/4)=0==>w=1
综上:w=1/3或1,y=3π/4或π/4
f(x)=sin(1/3x+3π/4)或f(x)=sin(x+π/4)
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