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

Problem

y=sin(π+3*x)

Solution

1. Rewrite the function in the standard form y=A*sin(B*(x−C))+D by rearranging the terms inside the sine function.

y=sin(3*x+π)

2. Factor out the coefficient of x to clearly identify the horizontal components.

y=sin(3*(x+π/3))

3. Identify the parameters A B and C from the standard form y=A*sin(B*(x−C))

A=1

B=3

C=−π/3

4. Calculate the amplitude using the absolute value of A

Amplitude=|1|=1

5. Calculate the period using the formula P=(2*π)/|B|

Period=(2*π)/3

6. Determine the phase shift from the value of C where a negative value indicates a shift to the left.

Phase Shift=−π/3

Final Answer

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

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