Cosines in a sentence

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.

In particular, only sines and cosines that map radians to ratios satisfy the differential equations that classically describe them.

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).

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.

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 ).

Re-writing sines and cosines as complex exponentials makes it necessary for the Fourier coefficients to be complex valued.

Sine and cosine transforms main Fourier's original formulation of the transform did not use complex numbers, but rather sines and cosines.

The obvious distinction between a DCT and a DFT is that the former uses only cosine functions, while the latter uses both cosines and sines (in the form of complex exponentials ).

The S scale has a second set of angles (sometimes in a different color), which run in the opposite direction, and are used for cosines.

The version with sines and cosines is also justified with the Hilbert space interpretation.

This means that these sines and cosines are different functions, and that the fourth derivative of sine will be sine again only if the argument is in radians.

This polynomial is irreducible over the rationals, and so these three cosines are conjugate algebraic numbers.

This space is actually a Hilbert space with an inner product given for any two elements f and g by : The basic Fourier series result for Hilbert spaces can be written as : Sines and cosines form an orthonormal set, as illustrated above.