函数y=arcsinx-arccosx,x∈[-1/2,√3/2]的值域是
设arcsinx=α,则arccosx=π/2-arcsinx=π/2-α;
故y=arcsinx-arccosx=α-(π/2-α)=2α-π/2;
由于-1/2≦x≦√3/2,故-π/6≦α≦π/3;-π/3≦2α≦2π/3;
于是得-π/3-π/2≦2α-π/2≦2π/3-π/2;即-5π/6≦2α-π/2≦π/6;
也就是-5π/6≦y≦π/6,这就是y的值域.
函数y=arcsinx-arccosx,x∈[-1/2,√3/2]的值域是
设arcsinx=α,则arccosx=π/2-arcsinx=π/2-α;
故y=arcsinx-arccosx=α-(π/2-α)=2α-π/2;
由于-1/2≦x≦√3/2,故-π/6≦α≦π/3;-π/3≦2α≦2π/3;
于是得-π/3-π/2≦2α-π/2≦2π/3-π/2;即-5π/6≦2α-π/2≦π/6;
也就是-5π/6≦y≦π/6,这就是y的值域.