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

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Answer 1 · 2015-02-26T21:02:40

The cotangent has no Amplitude, because it assumes every value in $(-oo,+oo)$ .

Let $f(x)$ be a periodic function:

$y=f(kx)$

has the period:

$T_f(kx)=T_f(x)/k$ .

So, since the cotangent has period $pi$ ,

$T_cot(2x)=pi/2$

The frequency is $f=1/T=2/pi$ .

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