Find Amplitude, Period, and Phase Shift f(x)=2sin(3x)

Problem

ƒ(x)=2*sin(3*x)

Solution

1. Identify the standard form of the trigonometric function, which is ƒ(x)=A*sin(B*(x−C))+D

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

|A|=|2|=2

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

P=(2*π)/3

4. Find the phase shift by identifying the horizontal displacement C Since there is no value subtracted from x inside the sine function, C=0

Phase Shift=0

Final Answer

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

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