What is the domain of the inverse sine function?

The correct choice indicates that the domain of the inverse sine function, also known as arcsine (denoted as sin⁻¹ or arcsin), falls within the interval from -1 to 1, inclusive. This range reflects the values that the sine function can take; since the sine function outputs values between -1 and 1 for all real numbers inputted into the function, the arcsine function can only accept inputs (i.e., its domain) within this same range.

Understanding this, if you input a value less than -1 or greater than 1 into the arcsine function, it would be undefined, as those values do not correspond to any angle whose sine value would equal them. Hence, the domain is correctly defined as the closed interval from -1 to 1.

While other options may imply different ranges, they do not align with the limits of the sine function. The importance of these domain restrictions is foundational in trigonometry and calculus, as they ensure that functions such as arcsin can operate correctly within prescribed boundaries.