By applying several matrix multiplications in succession, any vector can be expressed in any basis so long as the set of direction cosines is known relating the successive bases. Source: Internet
More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials ). Source: Internet
Re-writing sines and cosines as complex exponentials makes it necessary for the Fourier coefficients to be complex valued. Source: Internet
In particular, only sines and cosines that map radians to ratios satisfy the differential equations that classically describe them. Source: Internet
Introduction seeAlso In the first frames of the animation, a function f is resolved into Fourier series: a linear combination of sines and cosines (in blue). Source: Internet
It can also be used to find the cosines of an angle (and consequently the angles themselves) if the lengths of all the sides are known. Source: Internet