Question

函数fx=sin(π/4-x)(x∈[-π,0])的单调减区间是

Answer 1

f(x)=sin[-(x-π/4)]=-sin(x-π/4)；x∈[-π,0]时的单调递减区间为[-π/4,0]

∵f(-π)=-sin(-π-π/4)=sin(π+π/4)=-sin(π/4)=-√2/2；f(-π/4)=-sin(-π/4-π/4)=sin(π/2)=1；

f(0)=-sin(-π/4)=sin(π/4)=√2/2.