Find Amplitude, Period, and Phase Shift y=4cot(x)

Problem

y=4*cot(x)

Solution

1. Identify the standard form of the cotangent function, which is y=a*cot(b*(x−h))+k

2. Determine the amplitude. For trigonometric functions like cotangent, the amplitude is technically undefined because the function range is (−∞,∞) However, the vertical stretch factor is |a|=4

3. Calculate the period using the formula P=π/|b| In this equation, b=1

P=π/1=π

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

Final Answer

Amplitude: None (Vertical Stretch: 4), Period: *π*, Phase Shift: 0

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