Fourier Series Part 2 - Why both sines and cosines?
Channel: Gary Fox
Date: 15/10/2014

One of the really interesting things about sinusodial waves is if two waves with the same frequency are added together you get a third sinusodial wave of the same frequency.  
Because a Sine wave and a Cosine wave are 90 degrees out of phase with each other the summation of the two will create a wave with a phase somewhere between the sine and cosine.   In other words by looking at both the sine and cosine component we can determe the actual phase of the resultant wave.
The 90 degree phase difference between the sine and cosine is key to making the math really nice.  We are back to our old friend a 90 degree triangle.   The same thing we used when we analized beams and braces and many other things.
The blog post associated with this video is located at:  http://create-and-make.com/why-both-sines-and-cosines-with-the-fourier-series/  In that post I have included many links to previous posts on related topics, including some mechanical ones showing orthogonal components of an angle.