已知函数f(x)=sin(x+w)+3^(1/2)cos(x-w)为偶函数,求w的值已知函数f(x)=sin(x+w)+根号3cos(x-w)为偶函数,求w的值
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![已知函数f(x)=sin(x+w)+3^(1/2)cos(x-w)为偶函数,求w的值已知函数f(x)=sin(x+w)+根号3cos(x-w)为偶函数,求w的值](/uploads/image/z/6899215-31-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28x%2Bw%29%2B3%5E%281%2F2%29cos%28x-w%29%E4%B8%BA%E5%81%B6%E5%87%BD%E6%95%B0%2C%E6%B1%82w%E7%9A%84%E5%80%BC%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28x%2Bw%29%2B%E6%A0%B9%E5%8F%B73cos%28x-w%29%E4%B8%BA%E5%81%B6%E5%87%BD%E6%95%B0%2C%E6%B1%82w%E7%9A%84%E5%80%BC)
已知函数f(x)=sin(x+w)+3^(1/2)cos(x-w)为偶函数,求w的值已知函数f(x)=sin(x+w)+根号3cos(x-w)为偶函数,求w的值
已知函数f(x)=sin(x+w)+3^(1/2)cos(x-w)为偶函数,求w的值
已知函数f(x)=sin(x+w)+根号3cos(x-w)为偶函数,求w的值
已知函数f(x)=sin(x+w)+3^(1/2)cos(x-w)为偶函数,求w的值已知函数f(x)=sin(x+w)+根号3cos(x-w)为偶函数,求w的值
f(x)=f(-x)
sin(x+w)+sqrt(3)*cos(x-w)
=sin(w-x)+sqrt(3)*cos(x+w)
2(cos30度cos(x+w)-sin30度sin(x+w))=2(cos30度cos(x-w)+sin30度sin(x-w))
cos(x+w+30度)=cos(x-w-30度)
则x+w+30度=x-w-30度+2k*pi,k为整数
w=-30度+kpi
根据偶函数定义f(x)=f(-x)
整理等式得3^(1/2)cos(x+w)-sin(x+w)-[sin(x-w)+3^(1/2)cos(x-w)]=0
∴2[3^(1/2)/2cos(x+w)-1/2sin(x+w)]-2[1/2sin(x-w)+3^(1/2)/2cos(x-w)]=0
∴2cos(x+w+∏/6)-2sin(x-w+∏/3)=0
∴cos(x+...
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根据偶函数定义f(x)=f(-x)
整理等式得3^(1/2)cos(x+w)-sin(x+w)-[sin(x-w)+3^(1/2)cos(x-w)]=0
∴2[3^(1/2)/2cos(x+w)-1/2sin(x+w)]-2[1/2sin(x-w)+3^(1/2)/2cos(x-w)]=0
∴2cos(x+w+∏/6)-2sin(x-w+∏/3)=0
∴cos(x+w+∏/6)=sin(x-w+∏/3)=cos[∏/2-(x-w+∏/3)]
=cos(x-w-∏/6)
∴x+w+∏/6=x-w-∏/6
∴w=-∏/6
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