关於正弦函数的值域已知f(x)=2sin(x+π/6),当x∈[π/12,π/2],求f(x)的值域.

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关於正弦函数的值域已知f(x)=2sin(x+π/6),当x∈[π/12,π/2],求f(x)的值域.
关於正弦函数的值域
已知f(x)=2sin(x+π/6),当x∈[π/12,π/2],求f(x)的值域.

关於正弦函数的值域已知f(x)=2sin(x+π/6),当x∈[π/12,π/2],求f(x)的值域.
π/12

x∈[π/12,π/2]

π/12+π/6<=x+π/6<=π/2+π/6
则对2sin(x+π/6)
x=π/3时,取得最大值,2sin(π/3+π/6)=2sinπ/2=2
当x=π/12时,取得最小值,2sin(π/12+π/6)=2sinπ/4=√2

【根号2,2】

x∈[π/12,π/2]
x+π∈[π/4,2π/3]
根据正弦图像,sin(x+π/6),此区间内有最大值1,最小值是当x=π/4时=根号2/2
f(x) ∈[根号2,2]
ps:sorry,不会打根号