the problem is Given cos2x = 7/32, tan2x<0 and -\pi/2<x<\pi/2, find sin x

because

-\pi/2<x<\pi/2 means the answer would be either in the first or forth quadrant and tan2x has to be smaller than 0 so if the cos is positive, then the sin has to be negative?

Is this why there is only -5/8 as the answer instead of + or - 5/8 because of the square root when I took out the ?