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How is time averaged cos 2 ( Φ/2 ) is ½ ? i.e., how is cos 2 ( Φ/2 ) > is ½ where angular brackets represent time averaging?

How is time averaged cos2(Φ/2) is ½ ?
i.e., how is cos2(Φ/2)> is ½ where angular brackets represent time averaging?

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
If averaged over the complete period, it would also give zero as the time averages cos2(Φ/2).

But if solved for half the period, or using the even function property of the function, would be resolved to 1+cos(Φ) and integrated for half the period only. This result when averaged over the period over which it was integrated would result in ½.

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