函数y=sin(-2x+π/6)的单调递增区间是如题

函数y=sin(-2x+π/6)的单调递增区间是如题
函数y=sin(-2x+π/6)的单调递增区间是
如题

函数y=sin(-2x+π/6)的单调递增区间是如题
关键：把-2x+π/6看成sinx中的x
再利用正弦的单调性解决
2kπ-π/2< -2x+π/6

2kx-π/2<-2x+π/6<2kx+π/2
2kx-2*π/3<-2x<2kx+π/3
-kx+π/3>x>-kx-π/6

2kπ-π/2<=-2x+π/6<=2kπ+π/2
2kπ-2π/3<=-2x<=2kπ+π/3
-π/6-kπ<=x<=π/3-kπ (k为整数)

y=sinx 的单调减区间为[2kπ+π\2,2kπ+3π\2]
y=sin(-x) 的单调增区间为[2kπ+π\2,2kπ+3π\2]
∴2kπ+π\2≤-2x+π/6≤2kπ+3π\2
2kπ+π\3≤-2x≤2kπ+4π\3
kπ-2π\3≤x≤kπ-π\6
即x∈[kπ-2π\3,kπ-π\6]

－∏/2+2k∏≤－2x+∏/6≤∏/2+2k∏
得
X∈[－∏/6+k∏,∏/3+k∏]为其单调递增区间

2kx-π/2<-2x+π/6<2kx+π/2
2kx-2*π/3<-2x<2kx+π/3
-kx+π/3>x>-kx-π/6

2kπ-π/2<(-2x+π/6)<2kπ+π/2
2kπ-2π/3<(-2x)<2kπ+π/3
kπ-π/3<(-x)kπ-π/6