函数Y=sin(π/4-x)的单调增区间?

函数Y=sin(π/4-x)的单调增区间?
函数Y=sin(π/4-x)的单调增区间?

函数Y=sin(π/4-x)的单调增区间?
y=-sin(x-π/4)
令x-π/4=t
∴y=-sint
∴y的单调减区间为
2kπ-π/2≤t≤2kπ+π/2 k∈Z
2kπ-π/2≤x-π/4≤2kπ+π/2 k∈Z
2kπ-π/4≤x≤2kπ+3π/4 k∈Z
即y的单调减区间为[2kπ-π/4,2kπ+3π/4] k∈Z
∴ y的单调增区间为
2kπ+π/2≤t≤2kπ+3π/2 k∈Z
2kπ+π/2≤x-π/4≤2kπ+3π/2 k∈Z
2kπ+3π/4≤x≤2kπ+7π/4 k∈Z
即y的单调增区间为[2kπ+3π/4,2kπ+7π/4] k∈Z

y=sin(π/4+x/2)sin(π/4-x/2)
=-1/2(cosπ/2-cosx)
=1/2(cosx)
递增区间是x∈[2kπ+π,2(k+1)π] k∈Z