y=2sin(1\2x-π\3)+1
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y=2sin(1\2x-π\3)+1
(1)周期
(2)单调性
(3)最值
(1)周期
(2)单调性
(3)最值
y=2sin[(1/2)x-π/3]+1
(1)最小正周期:T=2π/(1/2)=4π.
(2)单调性:由2kπ-π/2≦(1/2)x-π/3≦2kπ+π/2,得2kπ-π/6≦(1/2)x≦2kπ+5π/6,得单增
区间为 4kπ-π/3≦x≦4kπ+5π/3;
由2kπ+π/2≦(1/2)x-π/3≦2kπ+3π/2,得2kπ+5π/6≦(1/2)x≦2kπ+11π/6,得单减区间为:
4kπ+π≦x≦4kπ+11π/3;
(3)最值:ymax=3,ymin=-1.
(1)最小正周期:T=2π/(1/2)=4π.
(2)单调性:由2kπ-π/2≦(1/2)x-π/3≦2kπ+π/2,得2kπ-π/6≦(1/2)x≦2kπ+5π/6,得单增
区间为 4kπ-π/3≦x≦4kπ+5π/3;
由2kπ+π/2≦(1/2)x-π/3≦2kπ+3π/2,得2kπ+5π/6≦(1/2)x≦2kπ+11π/6,得单减区间为:
4kπ+π≦x≦4kπ+11π/3;
(3)最值:ymax=3,ymin=-1.
y=2sin(1\2x-π\3)+1
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