Understanding the inverse sine function is essential for evaluating expressions involving trigonometric functions. The inverse sine function, denoted as sin^-1(x) or arcsin(x), is derived from the sine function by reflecting its graph over the line y = x. However, since the sine function is not one-to-one over its entire range, we restrict our focus to the interval from -π/2 to π/2 for the inverse sine function. This ensures that each input value corresponds to a unique output angle.

When evaluating inverse sine expressions, the input values must lie within the range of -1 to 1. The output angles, which are the results of the inverse sine function, will always fall within the specified interval of -π/2 to π/2. For example, to evaluate sin^-1(1/2), we seek an angle θ such that sin(θ) = 1/2. Referring to the unit circle, we find that θ = π/6 is the angle that satisfies this condition, as it lies within the required interval.

In another example, consider sin^-1(-√2/2). Here, we look for an angle θ where sin(θ) = -√2/2. The angle -π/4 meets this criterion, as it is located in the fourth quadrant and falls within the specified interval. Although 7π/4 also yields a sine value of -√2/2, it is outside the acceptable range for the inverse sine function.

In summary, when working with the inverse sine function, always ensure that the input values are between -1 and 1, and that the resulting angles are confined to the interval from -π/2 to π/2. This approach will facilitate accurate evaluations of inverse sine expressions.