求y=sin(派/4-2x)的单调区间

函数y=sin(π/4-2x)的单调递减区间
y=sin(π/4-2x)
=sin[-(2x-π/4)]
=-sin(2x-π/4)
要求y的单调递减区间,只需要求sin(2x-π/4)的单调递增区间即可
2kπ-π/2≤2x-π/4≤2kπ+π/2
kπ-π/8≤x≤kπ+3π/8 k∈z
同样要求y的单调递增区间,只需要求sin(2x-π/4)的单调递减区间即可
2kπ+π/2≤2x-π/4≤2kπ+3π/2
2kπ+π/4≤2x≤2kπ+7π/4
kπ+π/8≤x≤kπ+7π/8 k∈z
所以
函数y=sin(π/4-2x)的单调递减区间为[kπ-π/8,kπ+3π/8],k∈z
函数y=sin(π/4-2x)的单调递增区间为[kπ+π/8,kπ+7π/8],k∈z