Find Amplitude, Period, and Phase Shift y=-3cos(4x-8pi)

Problem

y=−3*cos(4*x−8*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 In this equation, A=−3 B=4 and C=8*π

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

Amplitude=|A|

Amplitude=|−3|=3

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

Period=(2*π)/4

Period=π/2

4. Find the phase shift by setting the argument of the cosine function to zero and solving for x or using the formula C/B

4*x−8*π=0

4*x=8*π

x=2*π

Final Answer

Amplitude=3,Period=π/2,Phase Shift=2*π

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