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

Problem

y=sin(x−π/6)

Solution

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

2. Determine the values of the constants from the given equation y=sin(1*(x−π/6))

3. Extract the parameters where A=1 B=1 C=π/6 and D=0

4. Calculate the amplitude using the formula Amplitude=|A|

|1|=1

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

(2*π)/1=2*π

6. Identify the phase shift using the value of C

π/6

Final Answer

Amplitude=1,Period=2*π,Phase Shift=π/6

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