Question

y=sin(π/4-2x)和y=cos(2x-π/3)求单调增区间.

Answer 1

y=sin(π/4-2x)单调增区间为

π/4-2x∈[2kπ-π/2,2kπ+π/2] (k∈Z)

-2x∈[2kπ-3π/4,2kπ+π/4] (k∈Z)

解得

x∈[kπ-π/8,2kπ+3π/8](k∈Z)

y=cos(2x-π/3)单调增区间为

2x-π/3∈[2kπ-π,2kπ] (k∈Z)

2x∈[2kπ-2π/3,2kπ+π/3] (k∈Z)

解得

x∈[kπ-π/3,kπ+π/6](k∈Z)