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

Problem

y=3*sin(2*x−π/3)

Solution

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

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

|A|=|3|

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

P=(2*π)/2

4. Find the phase shift by setting the argument of the sine function to zero and solving for x or using the formula C/B from the form y=A*sin(B*x−C)

2*x−π/3=0

2*x=π/3

x=π/6

Final Answer

Amplitude=3

Period=π

Phase Shift=π/6

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