Question

f(x)=sin(2x+3π/2)的单调区间？

Answer 1

f(x)=sin(2x+3π/2)的导数为2cos(2x+3π/2)，即f(x)的增减性取决于cos(2x+3π/2)的正负性。

当cos(2x+3π/2)>0时猛唤，即2x+3π/2在第一象限或第四象限，有2x+3π/2＜2π或2x+3π/2＞3π，解运嫌得x＜π/4或x＞5π/4。此时f(x)单调递增。

当cos(2x+3π/2)<0时，即2x+3π/2在第二象限或第三象限，有π/2＜旁知手2x+3π/2＜3π/2，解得π/4＜x＜5π/4。此时f(x)单调递减。

综上所述，f(x)=sin(2x+3π/2)的单调递增区间为x＜π/4或x＞5π/4，单调递减区间为π/4＜x＜5π/4。