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

Problem

y=2*cos(3*x)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where |A| is the amplitude, (2*π)/B is the period, and C is the phase shift.

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

|A|=|2|

|A|=2

3. Calculate the period using the formula (2*π)/B where B=3

Period=(2*π)/3

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=2,Period=(2*π)/3,Phase Shift=0

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