x[amplitude_,omega_,phase_,time_] := 
amplitude*Sin[omega*time + phase]

Manipulate[
Plot[
x[A,w,p,t],
{t,-20,20},
AxesLabel -> {"t","x = Asin(ωt + (Subscript[φ, 0]))"},
PlotRange -> {-2,2},
PlotStyle -> {Red,Thick}
],
{{A,1.0,Dynamic["Amplitude A"]},0.0,2.0,Appearance -> "Labeled"},
{{w,1.0,Dynamic["Angular Frequency ω"]},0.0,2.0,Appearance -> "Labeled"},
{{p,Pi,Dynamic["Phase Angle (Subscript[φ, 0])"]},0.0,2 Pi,Appearance -> "Labeled"}
]