要用到下面三行知识:
sin(x)的对称轴是 x = k*π + π/2, k为整数
sin(x)的单调递增区间为 2kπ - π/2 <= x <= 2kπ + π/2
sin(x)的单调递减区间为 2kπ + π/2 <= x <= 2kπ + 3*π/2
先求sin(2x+p)的对称轴。
即由2*x + p = k*π + π/2,求出x, x=1/2*k*π + π/4 - p/2.
由一条对称轴是x=π/8,带入上式,求出 p = k*π + π/4,
由p的取值范围知,k = -1,得到 p = -3/4*π
sin(2x+p) 的单调区间的求法:从下式解出x范围即可。
sin(x)的单调递增区间为 2kπ - π/2 <= 2x+p <= 2kπ + π/2
sin(x)的单调递减区间为 2kπ + π/2 <= 2x+p <= 2kπ + 3*π/2