Find Amplitude, Period, and Phase Shift y=-2cos(6x)

Problem

y=−2*cos(6*x)

Solution

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

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

|A|=|−2|

|A|=2

3. Determine the period using the formula P=(2*π)/|B| where B=6

P=(2*π)/6

P=π/3

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

Phase Shift=0

Final Answer

Amplitude=2,Period=π/3,Phase Shift=0

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