So you got .
There are two ways to think about this- the more formal is to use trig identities. You know, of course, that so that . Replacing t by arccos(x), and, of course, . That is, . Which sign is appropriate depends upon which quadrant you are in.
Less formal but perhaps simpler to see- imagine a right triangle with one angle y, "near side" of length x, and hypotenuse of length 1 (so that cos(y)= x/1= x). By the Pythagorean theorem, the "opposite side" has length so that and them which doesn't have the sign ambiguity because in setting up that right triangle we are assuming y is in the first quadrant.