Question

已知函數(shù)f(x)＝sinx＋cosx(x∈R)，函數(shù)y＝f(x＋φ)(|φ|≤)的圖象關(guān)于直線x＝0對稱，則φ的值為________．

Answer 1

f(x)＝2sin(x＋)，y＝f(x＋φ)＝2sin(x＋＋φ)的圖象關(guān)于x＝0對稱，即f(x＋φ)為偶函數(shù)．
∴＋φ＝＋kπ，k∈Z，φ＝kπ＋，k∈Z，
又|φ|≤，∴φ＝．