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

Problem

y=3*cos(π*x)

Solution

1. Identify the standard form of the trigonometric function y=A*cos(B*(x−C))+D where A is the amplitude, B is the frequency factor, C is the phase shift, and D is the vertical shift.

2. Determine the values of the constants from the given equation y=3*cos(π*x)

A=3

B=π

C=0

3. Calculate the amplitude using the absolute value of A

Amplitude=|A|

Amplitude=|3|=3

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

Period=(2*π)/π

Period=2

5. Determine the phase shift by identifying the horizontal displacement C

Phase Shift=0

Final Answer

Amplitude=3,Period=2,Phase Shift=0

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