Question

这道数学题求详细解答

Answer 1

(1)
周期π, ω = 2
一个对称中心为(π/4, 0), sin(π/2 + φ) = sin[π - {π/2 - φ)] = sin{π/2 - φ) = 0, φ = π/2 （在[0, π) 内的解)
f(x) = sin(2x + π/2)

x方向的变化相等于周期加倍, 即先变为sin(x + π/2), 再向右平移π/3，相当于x变为x - π/3,于是g(x) = sin(x - π/3 + π/2) = sin(x + π/6)

(2)
f(x)的对称轴为x = kπ/2, k为整数
对称中心为(kπ/2 + π/4, 0)

(3)
单调增: ((2k - 1)π, 2kπ)
单调减: (2kπ, (2k+1)π)