The domain of the function \( y = \sin x \) is all real numbers, denoted as \( (-\infty, \infty) \).
Explanation:
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Definition of the Sine Function: The sine function is defined for all real numbers \( x \). It takes an angle (measured in radians or degrees) and returns a value based on the unit circle.
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Graph of the Sine Function: The graph of \( y = \sin x \) is a continuous wave that oscillates between -1 and 1. It repeats every \( 2\pi \) radians. Since the function does not have any restrictions or points at which it is undefined, we can input any real number into the function.
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Mathematical Representation: Mathematically, you can express this domain in interval notation as \( (-\infty, \infty) \), indicating that the function accepts all real numbers.
In summary, because the sine function can take any real value as an input, its domain is all real numbers.