section_path: Applications/Periodic functions
section_name: Periodic functions
paragraph_text: Periodic functions
  
  The sine and cosine functions are fundamental to the theory of periodic functions, such as those that describe sound and light waves. Fourier discovered that every continuous, periodic function could be described as an infinite sum of trigonometric functions.
  
  Even non-periodic functions can be represented as an integral of sines and cosines through the Fourier transform. This has applications to quantum mechanics and communications, among other fields.