y=2sinx乘sin(π/3-x)值域如题
问题描述：
y=2sinx乘sin(π/3-x)值域
如题
答
积化和差：y=2sinxsin(π/3-x)＝-cos(π/3)＋cos(2x-π/3)＝-1/2＋cos(x-π/3)，-1≤cos(x-π/3)≤1，所以，y≤-1/2+1=1/2，y≥-1/2-1=-3/2，所以值域是[-3/2,1/2]
答
y=2sinx*sin(π/3-x)=2sinx*(√3/2cosx-1/2sinx)
=√3sinxcosx-sinx^2
=√3/2sin2x+1/2cos2x-1/2
=sin(2x+π/6)-1/2
sin(2x+π/6)∈[-1,1]
∴y∈[-3/2,1/2]