Find Amplitude, Period, and Phase Shift y=1/4*cos((2pi)/3x)

Problem

y=1/4*cos((2*π)/3*x)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=1/4 The amplitude is |A|

3. Calculate the amplitude:

Amplitude=1/4

4. Identify the value of B to find the period. Here, B=(2*π)/3

5. Apply the formula for the period, which is P=(2*π)/|B|

6. Calculate the period:

P=(2*π)/(2*π)/3

P=2*π⋅3/(2*π)

P=3

7. Identify the value of C to find the phase shift. Since there is no horizontal shift inside the argument of the cosine function, C=0

8. Calculate the phase shift:

Phase Shift=0

Final Answer

Amplitude=1/4,Period=3,Phase Shift=0

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