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

Problem

y=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 represents the coefficient of the cosine function. Here, A=1

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

Amplitude=|1|=1

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. Determine the value of C which represents the horizontal shift. Since there is no value subtracted from or added to x inside the function, C=0

7. Identify the phase shift as the value of C

Phase Shift=0

Final Answer

Amplitude=1,Period=2*π,Phase Shift=0

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