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f(x)=2sin·sin(π/3-x)的值域是多少呀
题目详情
f(x)=2sin·sin(π/3-x)的值域是多少呀
▼优质解答
答案和解析
f(x)=2sinx·sin(π/3-x)
=2sinx(sinπ/3cosx-cosπ/3sinx)
=√3sinxcosx-sin²x
=√3/2sin2x-1/2(1-cos2x)
=√3/2sin2x+1/2cos2x-1/2
=sin(2x-π/6)-1/2
f(x)max=1-1/2=1/2,
f(x)min=-1-1/2=-3/2
∴f(x)值域为[-3/2,1/2]
=2sinx(sinπ/3cosx-cosπ/3sinx)
=√3sinxcosx-sin²x
=√3/2sin2x-1/2(1-cos2x)
=√3/2sin2x+1/2cos2x-1/2
=sin(2x-π/6)-1/2
f(x)max=1-1/2=1/2,
f(x)min=-1-1/2=-3/2
∴f(x)值域为[-3/2,1/2]
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