Find Amplitude, Period, and Phase Shift y=1/4*cos(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, B affects the period, C is the phase shift, and D is the vertical shift.

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

|A|=|1/4|

Amplitude=1/4

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

Period=(2*π)/3

4. Find the phase shift by identifying the horizontal displacement C Since there is no value subtracted from or added to x inside the cosine function, C=0

Phase Shift=0

Final Answer

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

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