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, noting that the tangent function extends to positive and negative infinity. Therefore, the concept of amplitude does not apply to tangent functions in the same way it does to sine or cosine. The value is often described as undefined or none.

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

4. Identify the phase shift by looking at the horizontal displacement C Since the expression is x+π/2 the shift is π/2 units to the left.

Final Answer

Amplitude: None, Period: *π*, Phase Shift: −π/2

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