向量a=(√3,-sinwx/2),向量b=(sinwx,2sinwx/2)
f(x)=ab+m=√3sinwx-2sin^2wx/2+m
=√3sinwx-(1-coswx)+m
=√3sinwx+coswx-1+m
=2(√3/2sinwx+1/2coswx)+m-1
=2sin(wx+π/6)+m-1
w=2π/T=2π/3π=2/3
f(x)==2sin(2/3*x+π/6)+m-1,
X在[0,π]上f(x)最小值=0
-2+m-1=0
m=3
即有,w=2/3,m=3
2)f(x)==2sin(2/3*x+π/6)+2
(2a-√2c)cosB=√2bcosC
2sinAcosB-√2sinCcosB=√2sinBcosC
2sinAcosB-√2(sinCcosB+sinBcosC)=0
2sinAcosB-√2sin(C+B)=0
2sinAcosB-√2sinA=0
cosB=√2/2
B=π/4
A+C=3π/4
A=3π/4-C
f(A)=2sin(2/3*A+π/6)+2=2sin[2/3*(3π/4-C)+π/6]+2
=2sin[π/2-2/3*C+π/6]+2
=2cos(2/3*C-π/6)+2
C在(0,3π/4)
2/3*C-π/6在(-π/6,π/3)
f(A)=2cos(2/3*C-π/6)+2的值域为(3,4)
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