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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.

by Top Rated User (815k points)

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