Find Amplitude, Period, and Phase Shift y=1/4cos(3x)

Problem

y=1/4*cos(3*x)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where |A| is the amplitude, (2*π)/B is the period, and C is the phase shift.

2. Determine the value of A from the given equation y=1/4*cos(3*x)

A=1/4

3. Calculate the amplitude by taking the absolute value of A

Amplitude=|A|=1/4

4. Determine the value of B from the coefficient of x

B=3

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

Period=(2*π)/3

6. Determine the phase shift C Since there is no horizontal shift added or subtracted within the cosine argument, C=0

Phase Shift=0

Final Answer

Amplitude=1/4,Period=(2*π)/3,Phase Shift=0

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