In this example, the

amplitude `a = 12`, and
`b = 2`, so the period = `(2π)/b = (2π)/2 = π`, and

`c=-pi/8`

so the phase shift is

`-c/b=-(-pi"/"8)/2=pi/16`

This means we need to move the cosine graph to the right of its normal position (because the displacement is positive in this example) by `pi/16`.

Without phase shift, the cosine curve will be y = 12 cos 2x and its graph is as follows:

Graph y = 12 cos 2x

Now, let's shift it to the right by π/16 ≈ 0.1963:

shifted trigonometric graph

You can see the original cosine curve (in gray) and we have shifted it by `pi/16` to the right to give the required graph of `y = 12 cos (2x − π/8)`, in blue.

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