In this example, the
amplitude `a = 12`, and
`b = 2`, so the period = `(2π)/b = (2π)/2 = π`, and
so the phase shift is
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:
Now, let's shift it to the right by π/16 ≈ 0.1963:
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.