Question

The domain of y=cotx is all real numbers such that

A) The domain is all real numbers.
B) The domain is restricted to even multiples of pi/2.
C) The domain is limited to odd multiples of pi.
D) The domain consists of all real numbers except odd multiples of pi/2.

Answer 1

The domain of y = cot(x) consists of all real numbers except for odd multiples of pi/2, as cotangent is undefined when the tangent function is zero. Hence, the correct option is D.

Step-by-step explanation:

The domain of the trigonometric function cotangent, denoted as cot(x), refers to the set of all input values x for which the function is defined. The cotangent function is the reciprocal of the tangent function, which is undefined at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, ...), since the tangent function is zero at these points and division by zero is undefined in mathematics. Therefore, the correct answer to the given question is that the domain of the function y = cot(x) consists of all real numbers except for odd multiples of π/2, which aligns with option D.