Question

設(shè)函數(shù)y＝sin(ωx＋φ)(ω>0，φ∈(－，))的最小正周期為π，且其圖象關(guān)于直線x＝對(duì)稱，則在下面四個(gè)結(jié)論中：①圖象關(guān)于點(diǎn)(，0)對(duì)稱；②圖象關(guān)于點(diǎn)(，0)對(duì)稱；③在[0，]上是增函數(shù)；④在[－，0]上是增函數(shù)，所有正確結(jié)論的編號(hào)為________．

Answer 1

②④

∵T＝π，∴ω＝2．
又2×＋φ＝kπ＋，∴φ＝kπ＋．
∵φ∈(－，)，∴φ＝，∴y＝sin(2x＋)．
由圖象及性質(zhì)可知②④正確．