Time-Delay and Phase

It is always possible to rewrite a sinusoidal signal $x(t)=A \cos(2 \pi f_0t +\phi)$ in the form

$$x(t)=A \cos(2 \pi f_0(t-t_0)).$$ (1)

1.

Find a formula that describes the relationship between the phase $\phi$ and the delay t₀.

2.

Assume $x(t)=3\cos(2\pi 10 t + \frac{\pi}{4})$. Find the delay t₀ needed in the representation (1).

3.

Show that a sinusoid will always have a peak at t=t₀.