Find Amplitude, Period, and Phase Shift y=-4cos(pix)

Problem

y=−4*cos(π*x)

Solution

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

2. Determine the values of the constants from the given equation y=−4*cos(π*x) where A=−4 B=π C=0 and D=0

3. Calculate the amplitude using the formula Amplitude=|A|

Amplitude=|−4|=4

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

Period=(2*π)/π=2

5. Determine the phase shift using the value of C Since there is no horizontal shift inside the cosine function, the phase shift is 0

Phase Shift=0

Final Answer

Amplitude=4,Period=2,Phase Shift=0

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