求y=3sin(2x+π/4)的单调递增区间和y=3sin(2x+π/6)的单调递减区间

求y=3sin(2x+π/4)的单调递增区间和y=3sin(2x+π/6)的单调递减区间
求y=3sin(2x+π/4)的单调递增区间和y=3sin(2x+π/6)的单调递减区间

求y=3sin(2x+π/4)的单调递增区间和y=3sin(2x+π/6)的单调递减区间
y=sinx增区间[2kπ-π/2,2kπ+π/2]
所以本题,2kπ-π/2≤π/4+2x≤2kπ+π/2
kπ-3π/8

先用公式求周期T=2π/w,然后左右移动，最后乘以倍数。
按照这个步骤画图，由图得递增递减区间
书上有例题

[kπ-3π/8，kπ+π/8],k属于Z
[kπ+π/6,kπ+2π/3] ,k属于Z

2kπ-π/2≤2x+π/4≤2kπ＋π/2 解得kπ-3π/8≤x≤kπ+π/8 (k∈z)
2kπ+π/2≤2x+π/6≤2kπ+3π/2 解得kπ+π/6≤x≤kπ+2π/3 (k∈z)