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

Problem

y=tan(2*x−π/2)

Solution

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

2. Determine the amplitude. For the tangent function y=tan(x) the graph extends infinitely in both vertical directions, so the amplitude is undefined.

3. Calculate the period using the formula P=π/|B| In this equation, B=2

P=π/2

4. Find the phase shift by setting the argument of the tangent function to zero: 2*x−π/2=0

2*x=π/2

x=π/4

Final Answer

Amplitude: Undefined, Period: π/2*, Phase Shift: π/4

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