kosinuksen

Kosinus, often written as cos in mathematics, is the cosine function. In Finnish, kosinus denotes the same function, and kosinuksen is its genitive form, meaning “of the cosine” or “the cosine’s.” The cosine is defined for all real numbers and has a range between -1 and 1. It is an even, 2π-periodic function, satisfying cos(-x) = cos x and cos(x + 2π) = cos x.

Geometrically, cos x is the x-coordinate of the point on the unit circle corresponding to the angle x (measured in radians) from the positive x-axis.

Key identities include cos^2 x + sin^2 x = 1 and cos(a + b) = cos a cos b − sin a sin b. The derivative is -sin x and the integral is sin x + C. Values such as cos 0 = 1, cos π/2 = 0, and cos π = −1 are commonly used as reference points.

The Maclaurin series representation is cos x = 1 − x^2/2! + x^4/4! − ...; in the complex form, cos x = (e^{ix} + e^{−ix})/2.

Cosine plays a central role in trigonometry, physics, engineering, and signal processing, modeling periodic phenomena such as harmonic motion and serving in Fourier analysis and computer graphics. In discussions about the cosine, kosinuksen arvo refers to the numerical value of cos x for a given angle x.