Why does the trig expression just disappear?

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The discussion centers on the disappearance of a trigonometric expression in a solution involving time-averaging. It highlights that the expression (1 - cos(x)) becomes 1 when averaged over one period, specifically from 0 to 2π. This averaging process eliminates the trigonometric component, simplifying the equation. The mean-squared aspect is crucial in understanding this behavior. Overall, the conversion of the trig expression is linked to the properties of time-averaging in periodic functions.
adamaero
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Homework Statement


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Homework Equations



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3. Solution
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Then the equations from part (A) are used--but why does the converted trig (1-cos(etc)) go away?
Does this have to do with the mean-squared bit?
 

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Last edited:
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It becomes 1 when you time-average over one period.$$\frac{\int_0^{2\pi}(1-\cos x)dx}{\int_0^{2\pi}dx}=1$$
 
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