Find Amplitude, Period, and Phase Shift y=cos(5x)

Problem

y=cos(5*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(5*x) where A=1 B=5 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)/5

5. Calculate the phase shift using the value of C from the horizontal shift x−C

Phase Shift=0

Final Answer

Amplitude=1,Period=(2*π)/5,Phase Shift=0

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