There may be a "cleaner" way to do this, but from a practical standpoint you can just limit the range of your Sin function to [0,Pi) and create individual plots for a discrete values os "t" that you can later export as a list of images:
toexport =
Table[Plot3D[
Cos[\[Pi] (x^2 + y^2)/2] Sin[t], {x, y} \[Element] Disk[],
PlotRange -> {{-1, 1}, {-1, 1}, {-1.5, 1.5}}], {t, 0, Pi, 0.025}]
Export["mytest1.avi", toexport]
