Factor Out b First

In y = sin(2x - pi/2) it is tempting to read a shift of π/2. Check where the inside is zero: 2x − π/2 = 0 gives x = π/4. The wave starts at π/4, not π/2.

The way to see it at a glance is to take b out of the bracket:

sin(2x - pi/2) = sin(2(x - pi/4))

Now it reads as y = sin(b(x − h)): period 2π/2 = π, shift π/4 to the right. The shift is the number inside divided by b, because the squeezed wave covers ground twice as fast.