what is the range of the function $y = \\cot(x)$?\no all real numbers\no all real numbers except…

what is the range of the function $y = \\cot(x)$?\no all real numbers\no all real numbers except $\\frac{\\pi}{2}+n\\pi$, where $n$ is any integer\no all real numbers except $\\frac{n\\pi}{2}$, where $n$ is any integer\no all real numbers except $n\\pi$, where $n$ is any integer

what is the range of the function $y = \\cot(x)$?\no all real numbers\no all real numbers except $\\frac{\\pi}{2}+n\\pi$, where $n$ is any integer\no all real numbers except $\\frac{n\\pi}{2}$, where $n$ is any integer\no all real numbers except $n\\pi$, where $n$ is any integer

Answer

Answer:

A. all real numbers

Explanation:

Step1: Recall cotangent definition

$\cot(x)=\frac{\cos(x)}{\sin(x)}$

Step2: Analyze behavior

As $x$ varies, $\cot(x)$ can take on any real - valued output. The vertical asymptotes of $y = \cot(x)$ are at $x=n\pi$ ($n\in\mathbb{Z}$), but this affects the domain (not the range). The function $y = \cot(x)$ oscillates between $-\infty$ and $\infty$, so its range is all real numbers.