Inverse Function of a Trigonometric Function Game

The trigonometric functions are not invertible because they are not one-to-one (their graphs fail a horizontal line test). However, by restricting their domains, one can create restricted versions of these functions that are invertible, and the inverse trigonometric functions are thus defined. For example, the function is not one-to-one, but the function , , is one-to-one, and the function is the inverse of . For any function , , but since is not really the inverse of , but of its restriction, it is possible to have