Find Amplitude, Period, and Phase Shift y=1/4sin(5x+pi)

Problem

y=1/4*sin(5*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 P=(2*π)/|B| where B is the coefficient of x

B=5

Period=(2*π)/5

4. Find the phase shift by setting the argument of the sine function to zero and solving for x or using the formula Phase Shift=−C/B

5*x+π=0

5*x=−π

x=−π/5

Final Answer

Amplitude=1/4,Period=(2*π)/5,Phase Shift=−π/5

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