I am struggling with the following question.

The instantaneous power, p, in an electric circuit is given by p = iv,where v is the voltage and i is the current.

Calculate the maximum value of power in the circuit if

\(\displaystyle v = 0.02\sin (100\pi t)\) volts

\(\displaystyle i = 0.6\sin (100\pi t + \frac{\pi}{4} )\) amps

Calculate the first time that the power reaches a maximum value

I have started with the two multiplied together which makes

\(\displaystyle p = V(max) * I(max) \sin (100\pi t) \sin (100\pi t + \frac{\pi}{4} ) \)

Using the trigonometric formula 2.sin A.sin B = Cos(A-B) - Cos(A+B)

\(\displaystyle p = \frac{V(max) I(max)}{2} \cos 100\pi t - \frac{V(max) I(max)}{2} \cos (2 * 100\pi t + \frac{\pi}{4}) \)

therefore \(\displaystyle p = \frac{0.02 * 0.6 }{2} \cos 100\pi t - \frac{0.02 * 0.6V}{2} \cos (2 * 100\pi t + \frac{\pi}{4}) \)

I dont know what the next move is, or even if i am i going along the right lines??

Thanks for your help