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

Problem

y=cos(4*x)

Solution

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

2. Determine the values of the constants from the given equation y=cos(4*x) where A=1 B=4 C=0 and D=0

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

Amplitude=|1|=1

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

Period=(2*π)/4=π/2

5. Determine the phase shift using the value of C

Phase Shift=0

Final Answer

Amplitude=1,Period=π/2,Phase Shift=0

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