For the cosecant function, what is the domain?

The domain of the cosecant function is specifically determined by the fact that it is the reciprocal of the sine function. The cosecant function is defined as (csc(x) = \frac{1}{sin(x)}). Since division by zero is undefined, we need to identify where (sin(x) = 0), because at these points the cosecant function will also be undefined.

The sine function is equal to zero at integer multiples of (\pi), which can be expressed mathematically as (x = n\pi), where (n) is any integer. Thus, these values of (x) create discontinuities in the cosecant function, making them points that cannot be included in the domain.

The correct answer accurately reflects these restrictions, indicating that (x) cannot equal (n\pi), where (n) is any integer. Other choices suggest broader domains or different restrictions, which do not align with the behavior of the cosecant function.