Find Amplitude, Period, and Phase Shift y=sin(pi+6x)

Problem

y=sin(π+6*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(6*x+π)

2. Factor out the coefficient of x to clearly identify the horizontal compression and the phase shift.

y=sin(6*(x+π/6))

3. Identify the parameters from the standard form where A=1 B=6 and C=−π/6

A=1

B=6

C=−π/6

4. Calculate the amplitude, which is the absolute value of A

Amplitude=|1|=1

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

Period=(2*π)/6=π/3

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

Phase Shift=−π/6

Final Answer

Amplitude=1,Period=π/3,Phase Shift=−π/6

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