Find Amplitude, Period, and Phase Shift y=tan(x-pi/2)

Problem

y=tan(x−π/2)

Solution

1. Identify the standard form of the tangent function, which is y=A*tan(B*(x−C))+D In this equation, A=1 B=1 C=π/2 and D=0

2. Determine the amplitude, which is technically undefined for tangent functions because they extend to infinity. However, the vertical stretch factor is |A|

|A|=1

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

Period=π/1=π

4. Identify the phase shift by looking at the value of C in the expression (x−C)

Phase Shift=π/2

Final Answer

Amplitude: None (Stretch Factor: 1), Period: *π*, Phase Shift: π/2

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