已知向量m=(sinx,-1),向量n=(根号3cosx,-1/2),函数f(X )=m^2+m*n-2.求f(x)的最大值
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![已知向量m=(sinx,-1),向量n=(根号3cosx,-1/2),函数f(X )=m^2+m*n-2.求f(x)的最大值](/uploads/image/z/3741020-44-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fm%3D%28sinx%2C-1%29%2C%E5%90%91%E9%87%8Fn%3D%28%E6%A0%B9%E5%8F%B73cosx%2C-1%2F2%29%2C%E5%87%BD%E6%95%B0f%28X+%29%3Dm%5E2%2Bm%2An-2.%E6%B1%82f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC)
已知向量m=(sinx,-1),向量n=(根号3cosx,-1/2),函数f(X )=m^2+m*n-2.求f(x)的最大值
已知向量m=(sinx,-1),向量n=(根号3cosx,-1/2),函数f(X )=m^2+m*n-2.求f(x)的最大值
已知向量m=(sinx,-1),向量n=(根号3cosx,-1/2),函数f(X )=m^2+m*n-2.求f(x)的最大值
f(X )=m^2+m*n-2=sin^2x+1+ 根号3sinxcosx+1/2=sin^2x+ 根号3sinxcosx+3/2 =1/2(2sin^2x-1)+ 根号3sinxcosx+2=根号3/2sin2x-1/2cos2x+2=sin(2x-60)+2 1<=sin(2x-60)+2 <=3 最大值3