What is the domain of the cotangent function?

The cotangent function, defined as the ratio of the cosine to the sine function (cot(x) = cos(x)/sin(x)), has specific values where it is undefined. The sine function equals zero at integer multiples of π (nπ), which means that at these points, the value of the cotangent function cannot be computed - it results in a division by zero.

Thus, the domain of the cotangent function consists of all real numbers except for these points where the sine is zero. In other words, the cotangent function is defined for all real numbers x except for the values of nπ, where n is any integer (such as 0, ±1, ±2, etc.). This means option B accurately captures the restrictions on the domain of the function.

The other options do not accurately describe the domain of the cotangent function: "All reals" incorrectly includes the points where the function is undefined, "-1 to 1" suggests a limited interval that does not apply to the function's domain, and "None" is ambiguous and does not reflect the understanding of the function's behavior.