Graph y=2cos(x-pi/2)

Problem

y=2*cos(x−π/2)

Solution

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

2. Determine the amplitude |A| which is the distance from the midline to the peak. Here, A=2 so the amplitude is 2

3. Determine the period using the formula P=(2*π)/B Since B=1 the period is 2*π

4. Identify the phase shift C The expression x−π/2 indicates a horizontal shift to the right by π/2 units.

5. Identify the vertical shift D Since there is no constant added to the function, D=0 meaning the midline is the x-axis (y=0.

6. Find key points for one cycle by starting at the phase shift x=π/2 and adding increments of P/4=π/2

7. Calculate coordinates for the five key points:

(π/2,2)

(π,0)

((3*π)/2,−2)

(2*π,0)

((5*π)/2,2)

8. Plot the points and draw a smooth wave. Note that 2*cos(x−π/2) is equivalent to 2*sin(x) due to cofunction identities.

Final Answer

y=2*cos(x−π/2)=2*sin(x)

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