Find Amplitude, Period, and Phase Shift y=cos(6x)

Problem

y=cos(6*x)

Solution

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

2. Determine the coefficients from the given equation y=cos(6*x) where A=1 B=6 C=0 and D=0

3. Calculate the amplitude using the formula |A|

|1|=1

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

(2*π)/6=π/3

5. Calculate the phase shift using the value of C Since there is no horizontal shift inside the function, the phase shift is 0

Final Answer

Amplitude=1,Period=π/3,Phase Shift=0

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