Find Amplitude, Period, and Phase Shift y=3/2*cos((pix)/2)

Problem

y=3/2*cos((π*x)/2)

Solution

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

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

A=3/2

Amplitude=|A|=3/2

3. Calculate the period using the formula P=(2*π)/|B| where B is the coefficient of x

B=π/2

P=(2*π)/π/2

P=2*π⋅2/π=4

4. Find the phase shift by identifying the horizontal displacement C Since there is no value subtracted from x inside the cosine function, C=0

Phase Shift=0

Final Answer

Amplitude=3/2,Period=4,Phase Shift=0

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