How can I calculate average power for a trigonometric expression?

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Homework Help Overview

The discussion revolves around calculating the average power for a trigonometric expression involving sinusoidal functions, specifically 8sin(200t) and -6cos(200t - pi/4). The context is within electrical engineering, focusing on instantaneous voltage and power calculations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to combine the terms into a single expression with a common frequency and phase angle or to separate them into terms with different frequencies. They express difficulty in manipulating the trigonometric identities to achieve this. Some participants question whether the expression represents instantaneous power or voltage, leading to clarification on the actual variable being analyzed.

Discussion Status

Participants are exploring different methods to manipulate the trigonometric expression. One suggestion involves using a trigonometric identity to decompose the second term, which may help align the terms for further analysis. There is no explicit consensus on the best approach yet, but guidance has been offered regarding the decomposition of the cosine term.

Contextual Notes

There is a mention of a resistance value (R = 4 ohms) and a formula for power (P = 1/2 VI cos(theta - phi), indicating that the discussion may also involve considerations of phase angles and their impact on power calculations.

jesuslovesu
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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?
 
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jesuslovesu said:
8sin(200t) - 6 cos(200t - pi/4)

So is this supposed to be the instantaneous power?
 
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
 
You should decompose the second term using the following identity.

[tex]\cos(u-v)=\cos(u)\cos(v)+\sin(u)\sin(v)[/tex]

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

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