Find Amplitude, Period, and Phase Shift y=5/2*cos(x/2)

Problem

y=5/2*cos(x/2)

Solution

1. Identify the standard form of the trigonometric function, which is y=A*cos(B*(x−C))+D In this equation, A=5/2 B=1/2 C=0 and D=0

2. Calculate the amplitude by taking the absolute value of the coefficient A

Amplitude=|A|

Amplitude=|5/2|=5/2

3. Calculate the period using the formula P=(2*π)/|B|

Period=(2*π)/(1/2)

Period=4*π

4. Determine the phase shift by identifying the value of C in the argument. Since there is no horizontal shift added or subtracted from x the phase shift is zero.

Phase Shift=0

Final Answer

Amplitude=5/2,Period=4*π,Phase Shift=0

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