A Fourier series is a mathematical representation of a periodic function as a combination of sine and cosine functions. It allows us to break down a complex function into simpler components.
To calculate the Fourier series of a function, you need to find the coefficients for each sine and cosine term using integration. For a periodic function, the coefficients can be found using the Fourier series formula.
The Fourier series of sin^2(x) is (1/2) - (cos(2x)/2). This can be derived by using the trigonometric identity sin^2(x) = (1-cos(2x))/2 and applying the Fourier series formula.
The Fourier series of sin^2(x) is a representation of the original function as a combination of sine and cosine functions. By adding up all the terms in the series, we can recreate the original function.
The Fourier series allows us to break down a complex function into simpler components, making it easier to analyze and understand. It is also used in various fields such as signal processing, engineering, and physics to model and manipulate periodic functions.