Find Amplitude, Period, and Phase Shift y=1/4*sin(3x+pi)

Problem

y=1/4*sin(3*x+π)

Solution

1. Identify the standard form of the sine function, which is 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|=|1/4|

Amplitude=1/4

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

B=3

Period=(2*π)/3

4. Find the phase shift by solving the expression inside the sine function for zero, 3*x+π=0 or using the formula −C/B

3*x=−π

x=−π/3

Phase Shift=−π/3

Final Answer

Amplitude=1/4,Period=(2*π)/3,Phase Shift=−π/3

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