I got -30 and 19.5. I do think the sign is important as it indicates whether the angle is clockwise or anti-clockwise. I tried putting -19.5 and 30 into the calculator but they give sin with negative value.
you got -30 cause you did sin-1(-0.5) but, as you said, the negative is important IN GUIDING YOU.. that is to say, where the angle is negative.. like in the case of sin-1(1/3), the answer was 19.5 but you got positive value since it was sin-1 of 1/3 and not -1/3