The period is the distance between two peaks. We can ignore the amplitude 3.
4x+π/2=arcsin(-1)=-π/2+2πn where n is an integer.
Therefore 4x=-π+2πn, x=-π/4+πn/2.
x₀=-π/4, x₁=π/4, x₂=3π/4, ...
The gap between these x values is π/2, so π/2 is the period (frequency=2π/(π/2)=4).
sin(4x)=0 when x=0 and there is no phase shift. When x=p, where p is the phase shift, sin(4p+π/2)=0, 4p+π/2=0, p=-π/8. The phase shift is π/8.
