Find Amplitude, Period, and Phase Shift f(x)=3cos(4x-pi)+2

Problem

ƒ(x)=3*cos(4*x−π)+2

Solution

1. Identify the standard form of the trigonometric function, which is ƒ(x)=a*cos(b*x−c)+d

2. Extract the constants from the given equation: a=3 b=4 c=π and d=2

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

Amplitude=|3|=3

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

Period=(2*π)/4=π/2

5. Calculate the phase shift using the formula Phase Shift=c/b

Phase Shift=π/4

Final Answer

Amplitude=3,Period=π/2,Phase Shift=π/4

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