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

Problem

y=−2*cos(x)

Solution

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

2. Determine the value of A which is the coefficient of the cosine function. Here, A=−2

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

Amplitude=|−2|=2

4. Determine the value of B which is the coefficient of x Here, B=1

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

Period=(2*π)/1=2*π

6. Identify the phase shift C by looking at the horizontal displacement inside the function. Since there is no value subtracted from x C=0

Phase Shift=0

Final Answer

Amplitude=2,Period=2*π,Phase Shift=0

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