Let be the function defined on the interval by . The function is continuous and strictly increasing on , and . Therefore is invertible. Its inverse is called arcsinus and denoted .

For example: ; .

Let be the function defined on the interval by . The function is continuous and strictly decreasing on , and . Therefore is invertible. Its inverse is called arccosinus and denoted .

For example: ; .

Let be the function defined on the interval by . The function is continuous and strictly increasing on , and . Therefore is invertible. Its inverse is called arctangent and denoted .

For example: ; .

The inverse trigonometric functions verify many interesting identities; let us see some of them as examples.

- For any
, the following identity holds:

Therefore

It follows that . As belongs to the interval , we know that . Finally we have:

- For any
, the following identity holds:

Therefore

It follows that . As belongs to the interval , we know that . Finally we have: