Find Amplitude, Period, and Phase Shift y=sin(x+3)

Problem

y=sin(x+3)

Solution

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

2. Determine the amplitude by finding the absolute value of the coefficient A in front of the sine function.

|A|=|1|=1

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

Period=(2*π)/1=2*π

4. Determine the phase shift by solving the argument x+3=0 for x which corresponds to the value of C

x+3=0⇒x=−3

Final Answer

Amplitude: *1, Period: *2*π, Phase Shift: −3

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