Find Amplitude, Period, and Phase Shift y=1/4sin(x-pi/2)

Problem

y=1/4*sin(x−π/2)

Solution

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

2. Determine the amplitude by taking the absolute value of the coefficient A

|A|=|1/4|

Amplitude=1/4

3. Determine the period using the formula (2*π)/|B| In this equation, B=1

Period=(2*π)/1

Period=2*π

4. Determine the phase shift by identifying the value of C in the expression (x−C)

C=π/2

Phase Shift=π/2

Final Answer

Amplitude=1/4,Period=2*π,Phase Shift=π/2

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