求函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域要过程

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求函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域要过程求函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域要过程求函数y=2sin(2x+π/3),x属于(-π/6

求函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域要过程
求函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域
要过程

求函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域要过程
x∈(-π/6,π/6)
2x∈(-π/3,π/3)
2x+π/3∈(0,2π/3)
sin(2x+π/3)∈(0,1]
2sin(2x+π/3)∈(0,2]
所以函数y=2sin(2x+π/3),x属于(-π/6,π/6)的值域为:(0,2]

x属于(-π/6,π/6)
2x+π/3属于(0,2π/3)
值域(0,2]

x属于(-π/6,π/6)
(2x+π/3)属于(0,2π/3)
2sin(2x+π/3)属于(0,1]