Final question of my assigment, can anyone help me so I can celebrate!!

I'm struggling on the following question:

Power in an electric circuit is given by: p = iv

Calculate the maximum value of power if:

v = 0.002Sin (100piet)volts

i = 0.6Sin (100piet + pie/4)amps

and calculate the first time the power reaches a maximum value??

I've had a go at calculating maximum power and got the following:

0.6Sin(100piet + pie/4) x 0.02Sin(100piet)

= 0.012Sin(100piet) - Sin(100piet + pie/4)

= 1/2 x 0.012(cos(100piet -(100piet + pie/4))-cos(100piet+(100piet+pie/4))

= 0.006(cos pie/4 - cos(200piet + pie/4)

as smallest possible value is -1 for cos(200piet +pie/4)

: max value of p = 0.006(cos pie/4 +1)

= 0.0102?

Does this make any sense?

For the second part of the question: First time it reaches maximum power, I need some guidance on this one, I'm not sure where to go with this one?

All help would be greatly appreciated.