(a) to define the inverse sine function, we restrict the domain of sine to the interval . on this interval the sine function is one-to-one, and its inverse function sin−1 is defined by sin−1(x)

Domain is restricted to the range [-pi/2, pi/2] The sine function is a periodic function who's output ranges from -1 to 1 and back to -1. The inverse sine function can only accept values from the range -1 to 1 and each of the points within that range can theoretically represent any angle of the form X + n * pi where n is an integer. Since we can't have multiple return values for a function, we designate n to be 0 eliminating the periodic behavior and restrict the range of allowable angles to the range -pi/2 to pi/2 so we have a continuous function and an 1 to 1 mapping for sin(x) and sin^-1(x).