Trig function with shift

Hi guys I have a question in solving word trig function with shift.

I'm editing to be clearer.

When we are solving period for highest/lowest/midline period point (e.g., pi/2, 3pi/2 and pi, respectively for sine function). Why is it not enough to only equate period part of equation with above mentioned points, but you have to add whole period as well, with n coefficient (2pi n)

These questions are part of "Modelling with sinusoidal functions: phase shift" practice.

Thank you ;)