cosinussen

Cosinussen is the Dutch plural form of the cosine function and its values for angles. In Dutch mathematics, cosinussen refers to the cosine function applied to real or complex angles and to the set of its possible values.

Definition: For any angle θ, the cosinus (cos θ) can be defined geometrically as the x-coordinate of the point on the unit circle corresponding to angle θ, or in a right triangle as the ratio adjacent over hypotenuse.

Properties: The cosinus is an even function, meaning cos(-θ) = cos θ, and it is periodic with period 2π. Its range is [-1, 1]. Special values include cos 0 = 1, cos π/2 = 0, and cos π = -1. The graph of the cosinus is a smooth, continuous wave known as a cosine wave.

Formulas: The addition formula cos(a+b) = cos a cos b − sin a sin b, together with sin^2 θ + cos^2 θ = 1, are fundamental properties. Euler’s identity expresses cos θ as (e^{iθ} + e^{-iθ})/2, linking trigonometry to complex exponentials.

Applications: Cosinussen appear throughout mathematics and applied science, including solving triangles, modelling periodic phenomena, Fourier analysis, and signal processing. They underpin definitions of related functions and various techniques in physics and engineering.

Computation and inverse: The inverse function of the cosine, arccos, returns an angle from a cosine value within the interval [0, π]. The cosine can be computed by a series expansion: cos x = 1 − x^2/2! + x^4/4! − x^6/6! + ...

Notational note: In Dutch, cosinus is the singular form; cosinussen is the plural.