Find Amplitude, Period, and Phase Shift y=cot(2x)

Problem

y=cot(2*x)

Solution

1. Identify the function type and its standard form y=A*cot(B*(x−C))+D For the given function y=cot(2*x) we have A=1 B=2 C=0 and D=0

2. Determine the amplitude, which is technically undefined for the cotangent function because it does not have a maximum or minimum value. In the context of transformations, the vertical stretch factor is |A|=1

3. Calculate the period using the formula P=π/|B| Since B=2 the period is π/2

4. Find the phase shift by identifying the horizontal displacement C Since there is no value subtracted from or added to x inside the function, the phase shift is 0

Final Answer

Amplitude: None, Period: π/2*, Phase Shift: *0

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