求下列函数的最小正周期,值域,单调区间（1）y=sin(x+π/3) （2）y=2sin(1/2x-

求下列函数的最小正周期,值域,单调区间（1）y=sin(x+π/3) （2）y=2sin(1/2x-

(1) y = sin(x + π/3)最小正周期：T = 2π值域：y ∈ [-1 ,1]单调增区间：2kπ - π/2 ≤ x + π/3 ≤ 2kπ + π/2 ,x ∈[2kπ - 5π/6 ,2kπ + π/6]单调减区间：2kπ + π/2 ≤ x + π/3 ≤ 2kπ + 3π/2 ,x ∈[2kπ + π/6 ,2kπ + 7π/6](2) y = 2sin(1/2x - π/4) 最小正周期：T = 2π/(1/2) = 4π值域：y ∈ [-2 ,2]单调增区间：2kπ - π/2 ≤ x/2 - π/4 ≤ 2kπ + π/2 ,x ∈[4kπ - π/2 ,4kπ + 3π/2]单调减区间：2kπ + π/2 ≤ x/2 - π/4 ≤ 2kπ + 3π/2 ,x ∈[4kπ + 3π/2 ,4kπ + 7π/2](3) y=cos(2x - π/6）最小正周期：T = 2π/2 = π值域：y ∈ [-1 ,1]单调减区间：2kπ ≤ 2x - π/6 ≤ 2kπ + π ,x ∈[kπ + π/12 ,kπ + 7π/12]单调增区间：2kπ + π ≤ 2x - π/6 ≤ 2kπ + 2π ,x ∈[kπ + 7π/12 ,kπ + 13π/12](4) y=2cos(x - π/3) 最小正周期：T = 2π值域：y ∈ [-2 ,2]单调减区间：2kπ ≤ x - π/3 ≤ 2kπ + π ,x ∈[2kπ + π/3 ,2kπ + 4π/3]单调增区间：2kπ + π ≤ x - π/3 ≤ 2kπ + 2π ,x ∈[2kπ + 4π/3 ,2kπ + 7π/3](5) y=sin(2x - π/6) + 3 最小正周期：T = 2π/2 = π值域：y ∈ [-1 ,1]单调增区间：2kπ - π/2 ≤ 2x - π/6 ≤ 2kπ + π/2 ,x ∈[2kπ - π/6 ,2kπ + π/3]单调减区间：2kπ + π/2 ≤ 2x - π/6 ≤ 2kπ + 3π/2 ,x ∈[2kπ + π/3 ,2kπ + 5π/6](6) y = 3tan(2x - π/6)最小正周期：T = π/2值域：y ∈ (-∞ ,+∞)单调增区间：kπ - π/2 ======以下答案可供参考======供参考答案1:问老师去

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