Sinewaves and FFT plotter
Seems to me you just need to add the phase to the angle in update().
def update(val):
    amp = aslider.val
    freq = fslider.val
    phase = phslider.val
    t = np.linspace(0, 5, 200)

    y.set_ydata(amp*np.sin(2*np.pi*freq*t + phase))  # &lt;&lt; add phase here


fslider.on_changed(update)
aslider.on_changed(update)
tslider.on_changed(update)
pslider.on_changed(update)
phslider.on_changed(update)  # update on slider change