Finding formulas for sine and cosine functions:

[silvermane]

Homework Statement

Find simple formulas for
1+ cos(θ) + cos(2θ) + cos(3θ) + ... + cos(nθ)
and
sin(θ) + sin(2θ) + sin(3θ) + ... + sin(nθ)

The Attempt at a Solution

It's not really a homework question, but more for making a problem that I'm trying to solve a little bit more simple to calculate.

I know that 1 + x + x^2 + ... + x^n = [x^(n+1) - 1]/[x-1]

and I also know that u = cos(θ) + isin(θ)

I'm just having a little block in as how to incorporate these formulas to make my calculation a little easier.



You guys have always been great, and I do my best helping others with their combinatorics and linear algebra too. I know I'll get a wonderful answer, probably with some enrichment added on like icing to a cake. (just showing a little gratitude... I can't tell you how many times I've had wonderful educative experiences from this forum. It really does leave a positive mark on my life, lol)

Thank you in advance for your help! :) It means a lot to me!

 

[Dick]

Look at the sum e^(ik*theta) for k=0 to n. It's geometric isn't it?

 

[silvermane]

Yes it is - Thanks for jump starting my brain, haha

:)