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

Problem

y=cos(x−π/2)

Solution

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

2. Determine the parameters by comparing the given equation y=cos(x−π/2) to the standard form, where A=1 B=1 C=π/2 and D=0

3. Calculate the amplitude using the formula Amplitude=|A|

|1|=1

4. Calculate the period using the formula Period=(2*π)/|B|

(2*π)/1=2*π

5. Identify the phase shift, which is represented by the value of C

C=π/2

Final Answer

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

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