The inverse of a Function:
The corresponding to every bijection (oneone onto function) ƒ : A → B there exists a bijection g : B → A defined by
g(y) = x if and only if f(x) = y.
The function g : B → A is called the inverse of function ƒ : A → B and is denoted by ƒ^1.
We know that trigonometric functions are periodic functions and in general, all trigonometric functions are not bijections. Consequently, their inverses do not exist. However, if we restrict their domains and codomains, they can be made bijections and their inverses can be obtained.
The inverse trigonometric functions play an important role in calculus for they serve to define many integrals. The concepts of inverse trigonometric functions is also used in science and engineering.
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Formulas – Inverse Trigonometric Functions 
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