Find Amplitude, Period, and Phase Shift y=2cos(x-3)

Problem

y=2*cos(x−3)

Solution

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

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

|A|=|2|

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

P=(2*π)/1

4. Identify the phase shift C from the horizontal displacement within the argument (x−C)

C=3

Final Answer

Amplitude=2,Period=2*π,Phase Shift=3

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