Find Amplitude, Period, and Phase Shift y=-2cos(x/4)

Problem

y=−2*cos(x/4)

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 amplitude by taking the absolute value of the coefficient A=−2

Amplitude=|−2|=2

3. Calculate the period using the coefficient of x which is B=1/4

Period=(2*π)/(1/4)=8*π

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

Phase Shift=0

Final Answer

Amplitude=2,Period=8*π,Phase Shift=0

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