Find Amplitude, Period, and Phase Shift y=1/2*sin(2x+3pi)

Problem

y=1/2*sin(2*x+3*π)

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|=|1/2|

Amplitude=1/2

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

B=2

Period=(2*π)/2

Period=π

4. Find the phase shift by setting the argument of the sine function to zero and solving for x

2*x+3*π=0

2*x=−3*π

x=−(3*π)/2

Final Answer

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

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