Find Amplitude, Period, and Phase Shift y=1/2*cot(pix)

Problem

y=1/2*cot(π*x)

Solution

1. Identify the standard form of the cotangent function, which is y=A*cot(B*(x−C))+D

2. Determine the amplitude. For trigonometric functions like cotangent, the amplitude is technically undefined because the range is (−∞,∞) however, the vertical scaling factor is |A|=1/2

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

4. Substitute B=π into the period formula: P=π/π=1

5. Identify the phase shift C Since there is no horizontal shift added or subtracted within the argument of the cotangent function, C=0

Final Answer

Amplitude: None (Vertical Scale: 1/2*), Period: 1, Phase Shift: 0

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