Anyone know y I can use y(t)= Y=cos(wt + phi) to show phi= +/- cos^-1(y(0.00)/Y)? And why is the +/- needed?

Arc cos (0) = pi / 2. The +/- is phase difference. As for why you can use it in the first place to describe some motion in the y-direction, that's out of context and don't know. Could you be a little clearer pls?