Find Amplitude, Period, and Phase Shift y=3cos(1/2x)

Problem

y=3*cos(1/2*x)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where A=3 B=1/2 C=0 and D=0

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

Amplitude=|A|

Amplitude=|3|=3

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 horizontal displacement C

Phase Shift=C

Phase Shift=0

Final Answer

Amplitude=3,Period=4*π,Phase Shift=0

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