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What is the domain of the function [tex]y = \sin(x)[/tex]?

A. [tex]2 \pi[/tex]
B. [tex][0, \infty)[/tex]
C. [tex](-\infty, \infty)[/tex]
D. [tex][-1, 1][/tex]


Sagot :

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]