Find the sinusoidal function of V(t)

Question

Household electrical power in the US is provided in the form of alternating current. Typically, the voltage cycles smoothly between +155.6 volts and -155.6 volts 60 times per second. Use a sinusoidal function to model voltage, V, as a function of time, t, in seconds since the voltage was at its peak

V(t) = ?

Answer 1

let peak be at t=0

then in cos

v(t)=155.6cos(120πt),,,,,period =(1/60),,,,freq=2π/period

t=0, v=peak

in sin, must push peak at 1/240th second (phase shift) negative

v(t)=155.6sin(120π[t+1/240])

t=0,v=peak