Find Amplitude, Period, and Phase Shift y=-2cos(pix-3)

Problem

y=−2*cos(π*x−3)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D or y=A*cos(B*x−C)+D

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

Amplitude=|A|

Amplitude=|−2|=2

3. Calculate the period using the formula P=(2*π)/|B| where B is the coefficient of x which is π

Period=(2*π)/|B|

Period=(2*π)/π=2

4. Find the phase shift by setting the argument of the cosine function to zero: B*x−C=0

π*x−3=0

π*x=3

x=3/π

Final Answer

Amplitude=2,Period=2,Phase Shift=3/π

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