explain why sinx=1/2 has multiple answers but sin^1=1/2 (inverse sin) has one correct answer.

Answer 1

sinx = 1/2 has two answers (one in the 1st quadrant and one in the 2nd quadrant) because sine is positive in the 1st and 2nd quadrants.

inverse sine is restricted to the 1st and 4th quadrants, and since it is only positive in the 1st quadrant you only have one possible answer. Remember, inverses "switch" the domain and range, hence the restrictions to inverse sine.