To determine the domain and range of y = (sinx)^2.
The domain is the set of all real values of x for which the image or range or y values are real.
In (sinx)^2 , the variable x can can take any real value . So the domain is : - infinity < x < infinity.
The for any x, |sinx | < = 1.
Therefore forany x , 0 = < (sinx)^2 < = 1.
Therefore the range of the function is : 0 =< y < =1.
The function y = (sin x) ^2 is defined whenever sin x is defined, and its values are the squares of the values of sin x.
The domain of the function is the set of all real numbers. Since the values of sin x fill the interval from -1 to +1, and the square of a positive or a negative number is a positive number, the values of (sin x) ^2 fill the interval from 0 to 1.
Therefore the domain and range of the function is the set of all real numbers and the interval 0=< y <= 1, respectively.