Find Amplitude, Period, and Phase Shift y=6cos(2x)

Problem

y=6*cos(2*x)

Solution

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

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

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

Amplitude=|6|=6

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

Period=(2*π)/2=π

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

Phase Shift=0

Final Answer

Amplitude=6,Period=π,Phase Shift=0

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