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#.