已知向量a=(cos3/2x,sin3/2x),向量b=(cosx/2,-sinx/2),且x∈{-π/3,π/4},1.求向量a乘向量b及/向量a+向量b/2.若f(x)=向量a乘向量b - /向量a+向量b/,求f(x)最大值和最小值 求过程,谢谢拉~
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![已知向量a=(cos3/2x,sin3/2x),向量b=(cosx/2,-sinx/2),且x∈{-π/3,π/4},1.求向量a乘向量b及/向量a+向量b/2.若f(x)=向量a乘向量b - /向量a+向量b/,求f(x)最大值和最小值 求过程,谢谢拉~](/uploads/image/z/2524520-56-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos3%2F2x%2Csin3%2F2x%29%2C%E5%90%91%E9%87%8Fb%3D%28cosx%2F2%2C-sinx%2F2%29%2C%E4%B8%94x%E2%88%88%7B-%CF%80%2F3%2C%CF%80%2F4%7D%2C1.%E6%B1%82%E5%90%91%E9%87%8Fa%E4%B9%98%E5%90%91%E9%87%8Fb%E5%8F%8A%EF%BC%8F%E5%90%91%E9%87%8Fa%2B%E5%90%91%E9%87%8Fb%EF%BC%8F2.%E8%8B%A5f%28x%29%3D%E5%90%91%E9%87%8Fa%E4%B9%98%E5%90%91%E9%87%8Fb+-+%EF%BC%8F%E5%90%91%E9%87%8Fa%2B%E5%90%91%E9%87%8Fb%EF%BC%8F%EF%BC%8C%E6%B1%82f%28x%29%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC+%E6%B1%82%E8%BF%87%E7%A8%8B%EF%BC%8C%E8%B0%A2%E8%B0%A2%E6%8B%89%7E)
已知向量a=(cos3/2x,sin3/2x),向量b=(cosx/2,-sinx/2),且x∈{-π/3,π/4},1.求向量a乘向量b及/向量a+向量b/2.若f(x)=向量a乘向量b - /向量a+向量b/,求f(x)最大值和最小值 求过程,谢谢拉~
已知向量a=(cos3/2x,sin3/2x),向量b=(cosx/2,-sinx/2),且x∈{-π/3,π/4},
1.求向量a乘向量b及/向量a+向量b/
2.若f(x)=向量a乘向量b - /向量a+向量b/,求f(x)最大值和最小值
求过程,谢谢拉~
已知向量a=(cos3/2x,sin3/2x),向量b=(cosx/2,-sinx/2),且x∈{-π/3,π/4},1.求向量a乘向量b及/向量a+向量b/2.若f(x)=向量a乘向量b - /向量a+向量b/,求f(x)最大值和最小值 求过程,谢谢拉~
(1)a*b=cos3/2x*cosx/2-sin3/2x*sinx/2=cos(3/2x+x/2)=cos2x
/a+b/^2=(a+b)^2=a^2+b^2+2a*b=2+2cos2x=4cosx^2
又x∈{-π/3,π/4},cosx∈[1/2,1]
所以/a+b/=2cosx
(2)f(x)=a*b-/a+b/=cos2x-2cosx
=2cosx^2-2cosx-1 cosx∈[1/2,1]
令cosx=t,t∈[1/2,1]
y=2t^2-2t-1∈[-3/2,-1]
最大值为-1最小值为-3/2