What is the basis of inverse trigonometric functions?

Inverse trigonometric functions are primarily based on the radian measure. Radians are a natural way to measure angles in mathematics, particularly in the context of trigonometry. This is because the definition of the sine, cosine, and tangent functions—along with their inverses—originates from the unit circle, where angles are measured in radians.

Using radians allows for a more direct relationship between the angle measures and the lengths of the corresponding arcs and chords in the unit circle. When working with inverse trigonometric functions, the output values are often constrained within specific ranges, which are defined with the assumption that angles are in radians. This is why most tables and calculators for trigonometric functions and their inverses default to radians, making it crucial to understand this foundational aspect when dealing with these functions.

Degrees, gradians, and milliseconds are alternative units for measuring angles or time, respectively, but they do not align as naturally with the fundamental principles of trigonometry as radians do. Thus, when considering the basis of inverse trigonometric functions, radians stand out as the correct choice.