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}+npi), where (n) is any integer\no all real numbers except (\frac{npi}{2}), where (n) is any integer\no all real numbers except (npi), 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}+npi), where (n) is any integer\no all real numbers except (\frac{npi}{2}), where (n) is any integer\no all real numbers except (npi), where (n) is any integer

Answer

Explanation:

Step1: Recall cotangent function definition

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

Step2: Analyze its range

As $x$ varies, $\cot(x)$ can take on any real - valued output. The values for which $\cot(x)$ is undefined are the zeros of $\sin(x)$ (i.e., $x = n\pi$, $n\in\mathbb{Z}$), but these are domain restrictions, not range restrictions. The function $\cot(x)$ has no upper or lower bounds.

Answer:

all real numbers