Question

已知sinx*cosy=1/4,则siny*cosx的取值范围是

Answer 1

sinxcosy+cosxsiny=sin(x+y)

sinxcosy-cosxsiny=sin(x-y)

-1≤sin(x+y)≤1

-1≤1/4+cosxsiny≤1

-5/4≤cosxsiny≤3/4

-1≤sin(x-y)≤1

-1≤1/4-cosxsiny≤1

-5/4≤-cosxsiny≤3/4

-3/4≤cosxsiny≤5/4

综合得-3/4≤cosxsiny≤3/4