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

Problem

y=3*cos(2*x−π)

Solution

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

2. Extract the constants from the given equation y=3*cos(2*x−π) where A=3 B=2 and C=π

3. Calculate the amplitude by taking the absolute value of A

Amplitude=|A|

Amplitude=|3|=3

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

Period=(2*π)/B

Period=(2*π)/2=π

5. Calculate the phase shift using the formula C/B

Phase Shift=C/B

Phase Shift=π/2

Final Answer

Amplitude=3,Period=π,Phase Shift=π/2

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