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

Problem

y=4*cos(1/2*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. In this equation, A=4

3. Calculate the amplitude using the formula Amplitude=|A|

4. Determine the value of B to find the period. In this equation, B=1/2

5. Calculate the period using the formula Period=(2*π)/|B|

6. Determine the value of C to find the phase shift. Since there is no horizontal shift term inside the cosine, C=0

Final Answer

Amplitude=4

Period=4*π

Phase Shift=0

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