INVERSE TRIGONOMETRIC FUNCTIONS

The inverse trigonometric functions or cyclometric functions are the so-called inverse functions of the trigonometric functions, though they do not meet the official definition for inverse functions as their ranges are subsets of the domains of the original functions. Inverse trigonometric function returns an angle corresponding to a real number.
Every angle in the new domain (shortened) is related to a distinct real number in the range. Inversely, every real number in the range is related to a distinct angle in the domain of the trigonometric function. We are aware that the elements of the "ordered pair" in inverse relation exchanges their places. Therefore, it follows that domain and range of trigonometric function are exchanged for corresponding inverse function i.e. domain becomes range and range becomes domain.

Trigonometric functions are many-one relations. The trigonometric ratios of different angles evaluate to same value. The trigonometric functions are not an injection and hence not a bijection. As such, we can not define an inverse of trigonometric function in the first place! We shall see that we need to redefine trigonometric functions in order to make them invertible