You got it: is correct, sort of. The answer to your question has to do with the limited range of the inverse sine function.
The sine function in your problem has a period of 8 seconds, so whatever phenomenon you are investigating repeats every 8 seconds. It is at a position where when , so this is the solution to your equation. In order to answer your question you would have to be given more information as to which time is correct. For example, the problem statement may say to "look for the first solution after a half-minute".