Question

what are the zeros of a cotangent function? and does amplitude affect cotangent functions? ...?

Answer 1

$\cot{x}=0 \\ \\ \frac{\cos{x}}{\sin{x}} =0 \\ \\\cos{x}=0 \\ \\ x= k\pi, k \in Z$

The amplitude does not affect the zeroes of cotangent function.

$A\cot{x}=0 \Leftrightarrow \cot{x}=0$