Question

The domain of y = cot x is all real numbers such that:

a) x ≠ nπ, where n is an integer
b) x = nπ, where n is an integer
c) x ≠ (2n + 1)π/2, where n is an integer
d) x = (2n + 1)π/2, where n is an integer

Answer 1

The domain of y = cot x is all real numbers except for integral multiples of pi, where the function is undefined, so the answer is a) x ≠ nπ, where n is an integer.

Step-by-step explanation:

The domain of the function y = cot x includes all real numbers except for the points where the cotangent function is undefined. The cotangent of an angle x is the reciprocal of the tangent, and since tangent is sine over cosine, cot x is only undefined where sine is zero. The sine function equals zero at integral multiples of π, so the cotangent function is undefined when x = nπ, where n is an integer. Therefore, the correct answer is a) x ≠ nπ, where n is an integer.