# Trig average power Question

1. Apr 26, 2008

### jesuslovesu

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

2. Apr 26, 2008

### Tom Mattson

Staff Emeritus
So is this supposed to be the instantaneous power?

3. Apr 26, 2008

### jesuslovesu

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

4. Apr 26, 2008

### Tom Mattson

Staff Emeritus
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.