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shehry1
Oct29-08, 12:28 AM
Can anyone tell me what is the sum of a finite series of Sines.

\sum_{n=1}^N \sin^2 (n \phi) . I am going through a text and it gives it as (N+1)/2. I tried to derive it. The N comes out ok when you use the half angle identity but I can't figure out a general rule for the Cosines that appear

HallsofIvy
Oct29-08, 08:45 AM
What is \phi?

shehry1
Oct29-08, 11:13 AM
What is \phi?

\phi = \pi s /(N+1) where s = 1,2...N

tim_lou
Oct29-08, 02:09 PM
resolve sin^2 into 1-cos something. Put it in terms of complex exponentials. you'll get a geometric series.