Graph y=sin(2x-pi)

Problem

y=sin(2*x−π)

Solution

1. Identify the parent function and the general form of the sine equation y=A*sin(B*(x−C))+D

2. Factor the expression inside the sine function to identify the horizontal shift (phase shift) by rewriting 2*x−π as 2*(x−π/2)

y=sin(2*(x−π/2))

3. Determine the amplitude A which is the absolute value of the coefficient of the sine function.

|A|=1

4. Calculate the period using the formula P=(2*π)/B where B=2

P=(2*π)/2=π

5. Identify the phase shift C which is the horizontal displacement from the origin.

C=π/2* (to the right)

6. Determine the vertical shift D which is the constant added to the function.

D=0

7. Find the key points for one cycle by dividing the period into four equal intervals of π/4 starting from the phase shift x=π/2

(x_1)=π/2,(x_2)=(3*π)/4,(x_3)=π,(x_4)=(5*π)/4,(x_5)=(3*π)/2

8. Plot the points and draw a smooth sine wave through (π/2,0) ((3*π)/4,1) (π,0) ((5*π)/4,−1) and ((3*π)/2,0)

Final Answer

y=sin(2*x−π)

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