已知函数f(x)=√3sin2x-1/2(cos^2x-sin^2x)-1,x∈R,将函数f(x)向左平移π/6个单位后得到函数g(x)设△ABC的三个角A、B、C的对边分别为a,b,c.求:若g(B)=0且向量m=(cosA,cosB),向量n=(1,sinA-cosAtanB),
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 21:50:18
![已知函数f(x)=√3sin2x-1/2(cos^2x-sin^2x)-1,x∈R,将函数f(x)向左平移π/6个单位后得到函数g(x)设△ABC的三个角A、B、C的对边分别为a,b,c.求:若g(B)=0且向量m=(cosA,cosB),向量n=(1,sinA-cosAtanB),](/uploads/image/z/9315212-68-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%E2%88%9A3sin2x-1%2F2%28cos%5E2x-sin%5E2x%29-1%2Cx%E2%88%88R%2C%E5%B0%86%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E5%90%91%E5%B7%A6%E5%B9%B3%E7%A7%BB%CF%80%2F6%E4%B8%AA%E5%8D%95%E4%BD%8D%E5%90%8E%E5%BE%97%E5%88%B0%E5%87%BD%E6%95%B0g%EF%BC%88x%EF%BC%89%E8%AE%BE%E2%96%B3ABC%E7%9A%84%E4%B8%89%E4%B8%AA%E8%A7%92A%E3%80%81B%E3%80%81C%E7%9A%84%E5%AF%B9%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc.%E6%B1%82%EF%BC%9A%E8%8B%A5g%EF%BC%88B%EF%BC%89%3D0%E4%B8%94%E5%90%91%E9%87%8Fm%3D%EF%BC%88cosA%2CcosB%EF%BC%89%2C%E5%90%91%E9%87%8Fn%3D%281%2CsinA-cosAtanB%29%2C)
已知函数f(x)=√3sin2x-1/2(cos^2x-sin^2x)-1,x∈R,将函数f(x)向左平移π/6个单位后得到函数g(x)设△ABC的三个角A、B、C的对边分别为a,b,c.求:若g(B)=0且向量m=(cosA,cosB),向量n=(1,sinA-cosAtanB),
已知函数f(x)=√3sin2x-1/2(cos^2x-sin^2x)-1,x∈R,将函数f(x)向左平移π/6个单位后得到函数g(x)
设△ABC的三个角A、B、C的对边分别为a,b,c.求:若g(B)=0且向量m=(cosA,cosB),向量n=(1,sinA-cosAtanB),求向量m*向量n的取值范围(要详细步骤,
已知函数f(x)=√3sin2x-1/2(cos^2x-sin^2x)-1,x∈R,将函数f(x)向左平移π/6个单位后得到函数g(x)设△ABC的三个角A、B、C的对边分别为a,b,c.求:若g(B)=0且向量m=(cosA,cosB),向量n=(1,sinA-cosAtanB),
f(x)=(√3/2)sin2x-(1/2)cos2x-1=sin(2x-π/6)-1
左移π/6,
g(x)=sin2x-1
g(B)=0
B=π/4 tanB=1 cosB=√2/2
m*n=cosA+cosB*(sinA-cosA)
=cosBsinA+(1-cosB)cosA
=√[(cosB)^2+(1-cosB)^2] sin(A+u) cosu=cosB/√[(cosB)^2+(1-cosB)^2]=√2/2√(2-√2)
sinu=(1-cosB)/√[(cosB)^2+(1-cosB)^2]=(2-√2)/2√(2-√2)
=√[(1/2)+1+1/2-√2]sin(A+u)
=√(2-√2)sin(A-u)
A>0 sin(A-u)>sin(-u)=(√2-2)/[2√(2-√2)]
(2√2-3)/√(2-√2) < m*n