Find Amplitude, Period, and Phase Shift f(t)=2/3*cos(t)

Problem

ƒ(t)=2/3*cos(t)

Solution

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

2. Determine the value of A which is the coefficient of the cosine function. Here, A=2/3

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

Amplitude=|2/3|=2/3

4. Determine the value of B which is the coefficient of the variable t 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 t inside the cosine function, C=0

7. Identify the phase shift, which is equal to C

Phase Shift=0

Final Answer

Amplitude=2/3,Period=2*π,Phase Shift=0

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