Trigfunktio

Trigfunktio refers to a trigonometric function, a class of functions arising from ratios of the sides of a right-angled triangle or from coordinates on the unit circle. The term is frequently used in Scandinavian languages and is equivalent to the English "trigonometric function."

The primary trigonometric functions are sine, cosine, and tangent, which are defined for an angle θ as sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = sin θ / cos θ. Cosecant, secant, and cotangent are the reciprocals of sine, cosine, and tangent, respectively. Each function is periodic with period 2π radians, has a domain of all real numbers (except for secant, cosecant, and cotangent at points where cosine or sine equals zero), and a range that depends on the specific function (for example, sin and cos range between –1 and 1, while tan covers all real numbers).

Trigfunctions are intimately tied to the unit circle: the coordinates of a point on the circle at an angle θ provide the values of sine and cosine, and the slope of the line from the origin to that point gives the tangent. These relationships enable the derivation of addition formulas, double-angle identities, and power-reduction formulas.

Applications of trigfunctions span geometry, harmonic analysis, electrical engineering, and physics, where they model oscillatory phenomena, waveforms, and rotational motion. They also underpin Fourier analysis, signal processing, and the solutions of differential equations involving sinusoidal inputs.