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

1 Answer
Sep 2, 2016

Range: [-pi/2,pi/2]

Domain: [-1,1]

Explanation:

The following is a fragment from my lecture about y=arcsin x presented on UNIZOR.COM. If you go to this very useful Web site, click 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 y=sin(x) an interval of monotonic behavior is usually chosen as [−π/2,π/2], where the function is monotonously increasing from −1 to 1.

This variant of a sine function, reduced to an interval where it is monotonous and fills an entire range, has an inverse function called y=arcsin(x).

It has range [−π/2,π/2] and domain from -1 to 1.