Graph y=cos(x-pi/2)

Problem

y=cos(x−π/2)

Solution

1. Identify the parent function as y=cos(x) which has a period of 2*π an amplitude of 1 and starts at a maximum value of 1 at x=0

2. Determine the phase shift by looking at the horizontal translation inside the argument (x−π/2)

3. Calculate the shift value by setting the argument to zero: x−π/2=0⇒x=π/2 This indicates a horizontal shift to the right by π/2 units.

4. Apply the trigonometric identity cos(x−π/2)=sin(x) to simplify the graphing process.

5. Plot the key points for one period [π/2,(5*π)/2] the starting point (π/2,0) the maximum (π,1) the intercept ((3*π)/2,0) the minimum (2*π,−1) and the end of the cycle ((5*π)/2,0)

Final Answer

y=cos(x−π/2)=sin(x)

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