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

Problem

ƒ(x)=sin(3*x−2*π)

Solution

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

2. Determine the amplitude by taking the absolute value of the coefficient A in front of the sine function.

|A|=|1|=1

3. Determine the period using the formula P=(2*π)/|B| where B is the coefficient of x

P=(2*π)/3

4. Determine the phase shift by setting the argument of the sine function to zero and solving for x or using the formula C/B

3*x−2*π=0

⇒3*x=2*π

⇒x=(2*π)/3

Final Answer

Amplitude=1,Period=(2*π)/3,Phase Shift=(2*π)/3

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