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

Problem

y=sin(x−π/2)

Solution

1. Identify the standard form of the trigonometric function y=A*sin(B*(x−C))+D where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

2. Determine the amplitude by taking the absolute value of the coefficient A In this equation, A=1

|A|=|1|=1

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

P=(2*π)/1=2*π

4. Identify the phase shift C from the expression (x−C) In this equation, the term is (x−π/2) so C=π/2

C=π/2

Final Answer

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

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