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

Problem

y=3*cos(2*x+π)

Solution

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

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

|A|=|3|

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, 2*x+π=0 or using the formula Phase Shift=−C/B

Phase Shift=−π/2

Final Answer

Amplitude=3,Period=π,Phase Shift=−π/2

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