what is the period of the function y = cot x?

Explanation:

Step1: Recall cotangent function property

The cotangent function $y = \cot x=\frac{\cos x}{\sin x}$.

Step2: Use period - definition

We know that $\cot(x + \pi)=\frac{\cos(x+\pi)}{\sin(x + \pi)}$. Since $\cos(x+\pi)=-\cos x$ and $\sin(x+\pi)=-\sin x$, then $\cot(x+\pi)=\frac{-\cos x}{-\sin x}=\cot x$. And there is no positive number $T<\pi$ such that $\cot(x + T)=\cot x$ for all $x$ in the domain of $\cot x$.

Answer:

$1$