已知向量a=(2.cosx),向量b=(sin(x+π/6),函数f(x)=向量a*向量b(x属R)若f(x)=6/5 求cos(2x-π/3)的值打错了 向量b是(sin(x+π/6),-2)
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![已知向量a=(2.cosx),向量b=(sin(x+π/6),函数f(x)=向量a*向量b(x属R)若f(x)=6/5 求cos(2x-π/3)的值打错了 向量b是(sin(x+π/6),-2)](/uploads/image/z/8772386-50-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%EF%BC%882.cosx%29%2C%E5%90%91%E9%87%8Fb%3D%EF%BC%88sin%28x%2B%CF%80%2F6%EF%BC%89%2C%E5%87%BD%E6%95%B0f%28x%29%3D%E5%90%91%E9%87%8Fa%2A%E5%90%91%E9%87%8Fb%EF%BC%88x%E5%B1%9ER%EF%BC%89%E8%8B%A5f%28x%29%3D6%2F5+%E6%B1%82cos%EF%BC%882x-%CF%80%2F3%EF%BC%89%E7%9A%84%E5%80%BC%E6%89%93%E9%94%99%E4%BA%86++%E5%90%91%E9%87%8Fb%E6%98%AF%28sin%28x%2B%CF%80%2F6%29%2C-2%29)
已知向量a=(2.cosx),向量b=(sin(x+π/6),函数f(x)=向量a*向量b(x属R)若f(x)=6/5 求cos(2x-π/3)的值打错了 向量b是(sin(x+π/6),-2)
已知向量a=(2.cosx),向量b=(sin(x+π/6),函数f(x)=向量a*向量b(x属R)
若f(x)=6/5 求cos(2x-π/3)的值
打错了 向量b是(sin(x+π/6),-2)
已知向量a=(2.cosx),向量b=(sin(x+π/6),函数f(x)=向量a*向量b(x属R)若f(x)=6/5 求cos(2x-π/3)的值打错了 向量b是(sin(x+π/6),-2)
由题得,f(x)=2sin(x+π/6)-2cosx【2sin(x+π/6)=√3sinx+cosx,这个你应该能推算吧】
=√3sinx+cosx-2cosx
=√3sinx-cosx
=2sin(x-π/6)
因为f(x)=6/5,sin(x-π/6)=3/5
【下面用到这个公式估计你也学了吧,[sin(x/2)]^2=(1-cosx)/2】
[sin(x-π/6)]^2=1-cos(2x-π/3)=9/25,得
cos(2x-π/3)=16/25