已知函数f(x)=2sin(x+π/3)(1)求f(x)的单调增区间(2)当x∈[π/6,π/2]时,求f(x)的值域
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已知函数f(x)=2sin(x+π/3)(1)求f(x)的单调增区间(2)当x∈[π/6,π/2]时,求f(x)的值域
已知函数f(x)=2sin(x+π/3)
(1)求f(x)的单调增区间(2)当x∈[π/6,π/2]时,求f(x)的值域
已知函数f(x)=2sin(x+π/3)(1)求f(x)的单调增区间(2)当x∈[π/6,π/2]时,求f(x)的值域
(1) 令2kπ-π/2≤x+π/3≤2kπ+π/2,解得:2kπ-5/6*π≤x≤2kπ+π/6
所以单调递增区间为:[2kπ-5/6*π,2kπ+π/6] (k∈Z)
(2)当π/6≤x≤π/2时,π/2≤x+π/3≤5/6*π,1/2≤sin(x+π/3)≤1,即值域为:[1/2,1]
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