Find Amplitude, Period, and Phase Shift y=3cos(x/2)

Problem

y=3*cos(x/2)

Solution

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

2. Determine the value of A to find the amplitude. Here, A=3

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

Amplitude=|3|=3

4. Identify the value of B to find the period. Here, B=1/2

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

Period=(2*π)/(1/2)=4*π

6. Identify the value of C to find the phase shift. Since there is no horizontal shift inside the cosine function, C=0

Phase Shift=0

Final Answer

Amplitude: *3, Period: *4*π, Phase Shift: *0

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