Find the domain and range of y= (sin x) ^2

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neela | High School Teacher | (Level 3) Valedictorian

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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.

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william1941 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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