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

Problem

y=2*sin(3*x−π/2)+1

Solution

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

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

|A|=|2|

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

P=(2*π)/3

4. Find the phase shift by setting the argument of the sine function to zero and solving for x or using the formula C/B

3*x−π/2=0

3*x=π/2

x=π/6

5. Identify the vertical shift from the constant D added to the function.

D=1

Final Answer

Amplitude=2,Period=(2*π)/3,Phase Shift=π/6

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