what is the range of the cotangent function?\nthe range of the cotangent function is \n(type your answer in…

what is the range of the cotangent function?\nthe range of the cotangent function is \n(type your answer in interval notation.)

what is the range of the cotangent function?\nthe range of the cotangent function is \n(type your answer in interval notation.)

Answer

Explanation:

Step1: Recall cotangent function definition

The cotangent function is (y = \cot(x)=\frac{\cos(x)}{\sin(x)}).

Step2: Analyze its behavior

As (x) varies, (\sin(x)) and (\cos(x)) vary. The function (y = \cot(x)) has vertical - asymptotes at (x = n\pi), (n\in\mathbb{Z}). As (x) approaches (n\pi) from the left and right, (\cot(x)) approaches (-\infty) and (\infty) respectively.

Answer:

((-\infty,\infty))