Calculating Average Power Supplied from Phasors

[ineedmunchies]

Ok i have been given two trigonometric functions and asked to give them as phasors, and then calculate the average power supplied from this.

v = 311 sin (200t+7$$\circ$$) V

i = 14 sin (200t - 16$$\circ$$) A

I'm used to the trigonometric functions being in the cosine form, what difference will this make?

I believe it would be:
v = 311 $$\angle7$$
and i=14$$\angle-16$$

If it was given in the cosine form. And from there it would be possible to work out the average power.

Can anyone help me with this??

Also i know i might need to give the magnitude in RMS form.EDIT: Is it 83 degrees instead? and 74 for i?

 

[JaC82]

Cosine leads sine by 90 degrees. If you wanted to use cosine to represent v and i, you would subtract 90 degrees rather than add 90.

Vm = 311
Im = 14

To convert to phasor form multiply Vm and I am by .707

Veff = 219.877
Ieff = 9.898

The angles remain the same.

Pavg = Veff*Ieff*cos(theta), where theta is the phase angle between v and i.