已知向量a=(2sinx,cosx)b=(√3cosx,2cosx)定义f(x)=向量a*b-1求对称轴.
人气:287 ℃ 时间:2020-05-07 03:11:38
解答
f(x) = a.b-1
=(2sinx,cosx).(√3cosx,2cosx) -1
= 2sinxcosx + 2(cosx)^2 -1
= sin2x+cos2x
= sin(π/2-2x)+ cos(π/2-2x)
= sin2(π/4-x) + cos2(π/4-x)
f(x) = f(π/4-x)
f(π/8-x) = f(π/4-(π/8-x)
=f(π/8+x)
对称轴:y =π/8
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