若函数f(x)=根号3/2sin2x-1/2(cos^2*x-sin^2*x)-1,将函数f(x)向左平移π/6个单位后得到函数g_数学解答

若函数f(x)=根号3/2sin2x-1/2(cos^2*x-sin^2*x)-1,将函数f(x)向左平移π/6个单位后得到函数g（x）
①若c=根号7,f(C)=0,sinB=3sinA,求a,b的值?
②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?

人气：439 ℃　时间：2019-08-18 07:17:45

解答

f(X)=√3/2sin2x-1/2cos2x-1=sin(2x-π/6）-1
g(x)=f(x+π/6)=sin(2x+π/6)-1
①f(C)=sin(2C-π/6）-1=0
2C-π/6=π/2
C=π/3
sinB=3sinA=sin(A+C) 5/2sinA=√3/2cosA sinA=√21/14 sinB=3√21/14
有正弦定理得
a=3/4 b=9/4
②g(B)=0 B=π/6
m*n=cosA+√3/2(sinA-√3/3cosA)=√3/2sinA+1/2sinA=sin(A+π/6)∈ (0,1)