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

Problem

y=1/3*sin(x+π/2)

Solution

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

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

|A|=|1/3|

Amplitude=1/3

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

B=1

Period=(2*π)/1

Period=2*π

4. Find the phase shift by solving for x in the argument x+π/2=0

x=−π/2

Phase Shift=−π/2

Final Answer

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

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