Find Amplitude, Period, and Phase Shift f(x)=4sin(3x)

Problem

ƒ(x)=4*sin(3*x)

Solution

1. Identify the standard form of the sine function, which is ƒ(x)=A*sin(B*(x−C))+D In this specific function, A=4 B=3 C=0 and D=0

2. Calculate the amplitude by taking the absolute value of the coefficient A

Amplitude=|A|

Amplitude=|4|=4

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

Period=(2*π)/3

4. Determine the phase shift by identifying the horizontal displacement C Since there is no value subtracted from or added to x inside the sine function, the shift is zero.

Phase Shift=0

Final Answer

Amplitude=4,Period=(2*π)/3,Phase Shift=0

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