Homework Help: 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 =]