# Sum of a finite sine series

1. Oct 28, 2008

### shehry1

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

2. Oct 29, 2008

### HallsofIvy

Staff Emeritus
What is $\phi$?

3. Oct 29, 2008

### shehry1

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

4. Oct 29, 2008

### tim_lou

resolve sin^2 into 1-cos something. Put it in terms of complex exponentials. you'll get a geometric series.