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

Problem

y=2*sin(2*x−π/2)

Solution

1. Identify the standard form of the trigonometric function y=A*sin(B*(x−C))+D or y=A*sin(B*x−C)+D In this equation, A=2 B=2 and C=π/2

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

|A|=|2|=2

3. Calculate the period using the formula P=(2*π)/|B|

P=(2*π)/2=π

4. Find the phase shift by solving the expression inside the sine function for zero, or using the formula C/B

Phase Shift=π/2/2=π/4

Final Answer

Amplitude=2,Period=π,Phase Shift=π/4

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