Find the domain of definition of the following function y a

Find the domain of definition of the following function. y = arccos (sin^2 x).

Solution

sin(x) can take input for any real value of x and generates output real numbers from -1 to 1
so
-1<=sin(x)<=1
sin^2(x) will convert negative numbers into positive so
sin^2(x)<=1

value of sin^2(x) is the output for arccos( )
we know that domain of arccos( ) is all real numbers from -1 to 1
Since obtained values of sin^2(x) lies in -1 to 1
so there is no restriction on input value.

Hence domain of given function y=arccos(sin^2(x)) is all real numbers (R).