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

Problem

y=−2*cos(4*x+π)

Solution

1. Identify the standard form of the trigonometric function 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 where A=−2

Amplitude=|A|

Amplitude=|−2|=2

3. Calculate the period using the formula (2*π)/B where B=4

Period=(2*π)/B

Period=(2*π)/4=π/2

4. Find the phase shift by setting the argument of the cosine function to zero: 4*x+π=0

4*x=−π

x=−π/4

Final Answer

Amplitude=2,Period=π/2,Phase Shift=−π/4

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