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y=sin2x,x∈[-π/6,π/2]求值域
题目详情
y=sin2x,x∈[-π/6,π/2] 求值域
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答案和解析
-π/6<=x<=π/2
-π/3<=2x<=π
sin在(-π/2,π/2)递增,(π/2,3π/2)递减
所以2x=π/2时最大=sinπ/2=1
最小在边界
sin(-π/3)=-√3/2,sinπ=0
所以值域[-√3/2,1]
-π/3<=2x<=π
sin在(-π/2,π/2)递增,(π/2,3π/2)递减
所以2x=π/2时最大=sinπ/2=1
最小在边界
sin(-π/3)=-√3/2,sinπ=0
所以值域[-√3/2,1]
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