How can I calculate average power for a trigonometric expression?

[jesuslovesu]

Homework Statement

8sin(200t) - 6 cos(200t - pi/4)

Homework Equations

The Attempt at a Solution

I'm trying to calculate the average power for that expression so:
I need to get that expression into either one term with the same frequency and phase angle or two terms with a different frequency.
I've tried a bunch of different methods but can't quite get anything..

I've tried to turn 8sin(200t) into 4cos(100t)sin(100t) = 4cos(100t)cos(100t - pi/2) but then I get stuck with cosines multiplying each other.

Any help?

 

[quantumdude]

8sin(200t) - 6 cos(200t - pi/4)

So is this supposed to be the instantaneous power?

 

[jesuslovesu]

Thanks for your reply,

Sorry I kind of misspoke, it's actually instantaneous voltage,
vs = 8sin(200t) - 6cos(200t - 45 deg)
R = 4 ohms

P = 1/2 VI cos(theta - phi)

I think the best way to approach it would be to find it as an expression with two terms of different frequencies (so I can use superposition) but so far that hasn't worked

 

[quantumdude]

You should decompose the second term using the following identity.

$$\cos(u-v)=\cos(u)\cos(v)+\sin(u)\sin(v)$$

Then all of your time-dependent trig functions will have the same phase and frequency.