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

Problem

ƒ(x)=cot(x)

Solution

1. Identify the standard form of the cotangent function, which is ƒ(x)=a*cot(b*(x−h))+k For the given function ƒ(x)=cot(x) the parameters are a=1 b=1 h=0 and k=0

2. Determine the amplitude. For trigonometric functions like tangent and cotangent, the graph extends from negative infinity to positive infinity. Therefore, the concept of amplitude does not apply to these functions.

3. Calculate the period using the formula P=π/|b| Since b=1 the period is π

4. Find the phase shift using the value of h Since h=0 there is no horizontal displacement from the standard position.

Final Answer

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

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