# What is the amplitude, period and frequency for the function y=-1+\frac{1}{3} \cot 2x?

Feb 26, 2015

The cotangent has no Amplitude, because it assumes every value in $\left(- \infty , + \infty\right)$.

Let $f \left(x\right)$ be a periodic function:

$y = f \left(k x\right)$

has the period:

${T}_{f} \left(k x\right) = {T}_{f} \frac{x}{k}$.

So, since the cotangent has period $\pi$,

${T}_{\cot} \left(2 x\right) = \frac{\pi}{2}$

The frequency is $f = \frac{1}{T} = \frac{2}{\pi}$.