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

Problem

y=4*cos(2*x−π)

Solution

1. Identify the standard form of the trigonometric 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)/2

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

2*x−π=0

2*x=π

x=π/2

Final Answer

Amplitude=4,Period=π,Phase Shift=π/2

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