Find Amplitude, Period, and Phase Shift y=9/7cos(-(2pi)/7x)

Problem

y=9/7*cos(−(2*π)/7*x)

Solution

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

2. Apply the even property of the cosine function, cos(−θ)=cos(θ) to rewrite the expression as y=9/7*cos((2*π)/7*x)

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

|A|=|9/7|

Amplitude=9/7

4. Calculate the period using the formula P=(2*π)/|B| where B=(2*π)/7

P=(2*π)/(2*π)/7

P=2*π⋅7/(2*π)

Period=7

5. Find the phase shift by identifying the horizontal displacement C Since there is no constant added to or subtracted from the x term inside the cosine function, C=0

Phase Shift=0

Final Answer

Amplitude=9/7,Period=7,Phase Shift=0

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