what is the range of the function $y = cot(x)$?\nall real numbers\nall real numbers except…

what is the range of the function $y = cot(x)$?\nall real numbers\nall real numbers except $\frac{pi}{2}+npi$, where $n$ is any integer\nall real numbers except $\frac{npi}{2}$, where $n$ is any integer\nall real numbers except $npi$, where $n$ is any integer

what is the range of the function $y = cot(x)$?\nall real numbers\nall real numbers except $\frac{pi}{2}+npi$, where $n$ is any integer\nall real numbers except $\frac{npi}{2}$, where $n$ is any integer\nall real numbers except $npi$, 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 values that $\cot(x)$ cannot take do not exist in terms of range. The domain of $\cot(x)$ has restrictions ($x\neq n\pi$, $n\in\mathbb{Z}$ because $\sin(n\pi) = 0$ and division by zero is undefined), but the range is all real numbers.