## What are the Inverse Trigonometric Functions?

The inverse of a function f : A → B exists if *f* is one-one onto *i.e*., a bijection and is given by f(x) = y ⇒ f^{-1}(y) = x.

### Graphs of inverse trigonometric functions

### Domain and Range of inverse trigonometric functions

### Properties of inverse trigonometric functions

(5) **Principal values for inverse circular functions:**

(6)** Conversion property:**

(7) **General values of inverse circular functions: **We know that if ?

*is the smallest angle whose sine is*

*x*, then all the angles whose sine is

*x*can be written as nx + (−1)

^{n}? where n = 0, 1, 2, ……. Therefore, the general value of sin

^{−}

^{1}x can be taken as nx + (−1)

^{n}?. The general value of sin

^{−}

^{1}x is denoted by sin

^{−}

^{1}x.

Thus, we have

Similarly, general values of other inverse circular functions are given as follows:

### Formulae for sum, difference of inverse trigonometric function

### Inverse trigonometric ratios of multiple angles