# What is the domain and range of #y = arcsin x#?

##### 1 Answer

Range:

Domain:

#### Explanation:

The following is a fragment from my lecture about *Trigonometry - Inverse Trigonometric Functions - y=arcsin(x)*.

The original *sine* function defined for any real argument does not have an inverse function because it does not establish a one-to-one correspondence between its domain and a range.

To be able to define an inverse function, we have to reduce the original definition of a *sine* function to an interval where this correspondence does take place. Any interval where *sine* is monotonic and takes all values in its range would fit this purpose.

For a function

This variant of a *sine* function, reduced to an interval where it is monotonous and fills an entire range, has an inverse function called

It has range