# Sum of Discrete Sinusoids

1. Mar 13, 2014

### Superman1271

1. The problem statement, all variables and given/known data

Hi Everyone, I am trying to show why the given sum is zero. I am pretty sure it is zero.

2. Relevant equations

sin[8*$\pi$*n/5]+sin[12*$\pi$*n/5]

n is an integer.

3. The attempt at a solution

n----sin[8*$\pi$*n/5]----sin[12*$\pi$*n/5]

0 ---- 0------------------------------ 0

1 ---- -0.9511------------------------ 0.9511

2 ---- -0.5878------------------------ 0.5878

3 ---- 0.5878------------------------ -0.5878

4 ---- 0.9511------------------------ -0.9511

5 ---- 0------------------------------- 0

I am looking for an analytic solution thank you.

2. Mar 13, 2014

### Dick

It's because the point between those two numbers is 10*pi*n/5=2*pi*n. Enough of a hint?

Last edited: Mar 13, 2014
3. Mar 14, 2014

### HallsofIvy

The point exactly half way between those two numbers is 2pi n.

4. Mar 14, 2014

### Superman1271

So on the unit circle the halfway point is always along the positive x-axis. And if that is halfway, the y components will always be the negative of eachother?

Also how did you realize it was exactly half way?

5. Mar 14, 2014

### Dick

Thinking about where the points for various n lie on the unit circle is a good way.

6. Mar 15, 2014

### Superman1271

Ok, Thanks =]