The function [tex]\( y = \sin(x) \)[/tex] is known as the sine function, which is a fundamental function in trigonometry.
To determine the domain of this function, we need to identify the set of all possible input values [tex]\( x \)[/tex] for which the function [tex]\( y = \sin(x) \)[/tex] is defined.
1. The sine function is defined for all real numbers. It does not have any restrictions or undefined points.
2. Therefore, regardless of the value of [tex]\( x \)[/tex] that you input into the function, [tex]\( \sin(x) \)[/tex] will give you a real number.
Thus, the correct domain of the function [tex]\( y = \sin(x) \)[/tex] is all real numbers. Mathematically, this is represented as:
[tex]\[ (-\infty, \infty) \][/tex]
Therefore, the correct answer is:
C. [tex]\((- \infty, \infty)\)[/tex]
