y=2sinx乘sin(π/3-x)值域如题

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 00:56:55
y=2sinx乘sin(π/3-x)值域如题y=2sinx乘sin(π/3-x)值域如题y=2sinx乘sin(π/3-x)值域如题y=2sinx*sin(π/3-x)=2sinx*(√3/2cosx

y=2sinx乘sin(π/3-x)值域如题
y=2sinx乘sin(π/3-x)值域
如题

y=2sinx乘sin(π/3-x)值域如题
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]

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]