求y=sinx/2-cosx的值域

1个回答

  • y=sinx/2-cosx

    =sin(x/2)-[1-sin²(x/2)]/2

    =sin(x/2)-1/2+sin²(x/2)/2

    =1/2[sin²(x/2)+2sin(x/2) +1]-1

    =1/2[sin(x/2) +1]²-1

    由-1≤sin(x/2) ≤1得

    sin(x/2)=-1时,取得最小值-1

    sin(x/2)=1时,取得最大值1

    所以值域为[-1,1]