Find Amplitude, Period, and Phase Shift y=4cos(3x+pi/2)

Problem

y=4*cos(3*x+π/2)

Solution

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

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

|A|=|4|

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

P=(2*π)/3

4. Find the phase shift by setting the argument of the cosine function to zero and solving for x or using the formula Phase Shift=−C/B

3*x+π/2=0

3*x=−π/2

x=−π/6

Final Answer

Amplitude=4,Period=(2*π)/3,Phase Shift=−π/6

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